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UTPA STEM/CBI Courses/Physics (Calculus Based)/Circular Motion

Course Title: Calculus Based Physics I

Lecture Topic: Circular Motion

Instructor: Liang Zeng

Institution: University of Texas-Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Know why an object goes in circular motion (centripetal force, constantlypointing towards the center of the circle)
 * Know how to analyze and calculate the resultant force, centripetal force and acceleration
 * Know how to calculate instantaneous velocity (along tangential line)
 * Know how to convert degrees to radians and revolutions to radians
 * Know how to calculate angular velocity and determine its direction
 * Know how to calculate angular acceleration and determine its direction from the resultant force
 * Know how to do cross product using the right hand rule (pay attention to unit vectors)
 * Know how to use the right-hand rule to determine the direction of velocity
 * Know how to do rotational kinematics with constant angular acceleration
 * Compare angular kinematics with translational kinematics

 * Sub Objectives- The objectives will require that students be able to:
 * text
 * text

 * Difficulties- Students may have difficulty:
 * Finding centripetal force on a banked surface ( students need to be taught how to determine the direction of normal force, direction of centripetal force pointing towards a virtual center on a horizontal plane)
 * The direction of angular velocity (curl four fingers and thumb points toward angular velocity)
 * Right-hand rule (cross-product) applied to rigid bodies such as a spinning wheel
 * Determining the direction of instantaneous velocity (along the tangential line)

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Drive a car and turn a sharp curve (easier to turn a large curve than a sharp curve)*
 * Banked curve versus unbanked curve simulation
 * Centrifuge (biology & chemistry labs, separate particles of different density, set test tube at an angle)*
 * Hula hoop
 * CD player
 * Pilots fly loop-the-loop
 * Roller coaster
 * Merry-go-round
 * Spinning wheels: bicycle and car wheels, hands of a watch, big gears in big motors, fly wheel in a boat
 * Earth's spin around its own axis, spinning top
 * Satellite goes almost circular motions
 * Swing something attached to a cord

Model of Knowledge

 * Concept Map
 * text
 * text
 * text

 * Content Priorities
 * Enduring Understanding
 * Centripetal force, centripetal acceleration (how to calculate them)
 * Centrifugal phenomena
 * Conversion of units from degrees to radians, angular displacement
 * Determining magnitude of angular velocity
 * Relation between angular velocity and instantaneous velocity and their directions (right hand rule, cross product)
 * Rotational kinemtaic equations
 * Comparison between rotational and translational kinematic equations
 * Important to Do and Know
 * Identify the normal force at different locations on a circular loop
 * Analyze the normal force for more complicated multi-curve problems, such as roller coasters
 * Worth Being Familiar with
 * Elliptical motion: Earth revolves around the Sun, Sun is in one of the foci
 * Radial and tangential acceleration, example birds scoop up fish and fly away

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * text
 * text
 * Homework (individual)
 * text
 * text
 * Summative Assessment
 * text
 * text

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * text
 * text
 * text
 * text
 * text
 * text

THE CHALLENGE

Instructions:students can refer to any resource to answer this question. Each person needs to scan and save the report as a pdf file, and email the report to Mr. Manuel Lara, Teaching Assistant on WebCT which answers the question with supporting data linking back with the relevant physics content. The report is usually due a week from the date when the question is assigned and will be kept in a WebCT folder. Rubric for grades (on a 0-10 point scale): 1. Correct solution for how a passenger feels at any time on the ride and how the force a passenger feels changes over different positions along the track (4 points). 2. Correct solution for the relationship between the angular speed of the apparatus and the position of the ball-shaped room (4 points). 3. Reasonable analysis for the maximum allowable angular speed of the apparatus (2 points). Format: 1. Put down your name. 2. State challenge question and its number. 3. Show all your work.

Challenge Question #5: As an engineer for Disney World you are asked to design a new amusement ride. This device consists of a ball-shaped room where the passengers strap themselves to seats. The ball is placed in a hemispherical bowl-shaped apparatus. When the apparatus is rotating the ball is allowed to move up along the wall of the apparatus by means of a track that extends from the bottom of the apparatus to the top. Suppose the mass of the ball including the passengers is m and suppose the radius of the ball is much smaller than the radius of the apparatus. Analyze how a passenger feels at any time on the ride and how the force a passenger feels changes over different positions along the track? What is the relationship between the angular speed of the apparatus and the position of the ball-shaped room? To ensure that none of the passengers blacks out or loses consciousness during the ride, what is the maximum allowable angular speed of the apparatus? Show all you mathematical work to support your analysis and descriptions.

GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Pre-Lesson Quiz

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Test Your Mettle Quiz
1.(Centripetal force, banked surface: Knight 2nd edition page 231 #8). A highway curve of radius 500 m is designed for traffic moving at 90 km/hr. What is the correct banking angle of the road?

2.(Centripetal force, unbanked surface: Knight 2nd edition page 231 #5). A 1500 kg car takes a 50-m-radius unbanked curve at 15 m/s. What is the size of the friction force on the car?

3.(Centripetal force, looped surface: Knight 2nd edition page 233 #41). In an amusement park ride called the Roundup, passengers stand inside a 16-m-diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure.

a)Suppose the ring rotates once every 4.5 s. If a rider’s mass is 55 kg, with how much force does the ring push on her at the top of the ride? At the bottom?

b)What is the longest rotational period of the wheel that will prevent the riders from falling off at the top?

4.(Centripetal force, tension in a cord, horizontal plane: Serway 7th edition page 159 #50). An air puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a frictionless horizontal table. The other end of the string passes through a small hole in the center of the table, and a load of mass m2 is tied to the string, as shown in the figure. The suspended load remains in equilibrium while the puck on the tabletop revolves.

a)What is the tension in the string?

b)What is the radial force acting on the puck?

c)What is the speed of the puck?

d)Qualitatively describe what will happen in the motion of the puck if the value of m2 is somewhat increased by placing an additional load on it.

e)Qualitatively describe what will happen in the motion of the puck if the value of m2 is instead decreased by removing a part of the hanging load.

5.(Centripetal force, tension in a cord, at angle to horizontal plane: Serway 7th edition page 160 #53). An amusement park ride consists of a rotating circular platform 8.00 m in diameter from which 10.0-kg seats are suspended at the end of 2.50-m massless chains, as shown in the figure. When the system rotates, the chains make an angle θ = 28.0° with the vertical.

a)What is the speed of each seat?

b)Draw a free-body diagram of a 40.0-kg child riding in a seat and find the tension in the chain.

6.(Centripetal acceleration, conceptual: Knight 2nd edition page 230 #3). The following figure is a bird’s eye view of particles moving in horizontal circles on a tabletop (scan and insert figure). All are moving at the same speed.

a)Rank in order, from largest to smallest, the tensions Ta to Td. Give your answer in the form a > b = c > d and explain your ranking.

b)Calculate the angular speeds ωa, ωb, ωc, and ωd.

7(Rotational kinematics with constant acceleration: Serway 7th edition page 300 #6). A rotating wheel requires 3.00 s to rotate through 37.0 revolutions. Its angular speed at the end of the 3.00-s interval is 98.0 rad/s. What is the constant angular acceleration of the wheel?

8.(Multi-curve problem: Serway 7th edition page 156 #14). A roller-coaster car (see figure below) has a mass of 500 kg when fully loaded with passengers.

a)If the vehicle has a speed of 20.0 m/s at point  A , what is the force exerted by the track on the car at this point?

b)What is the maximum speed the vehicle can have at point  B   and still remain on the track?


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UTPA STEM/CBI Courses/Physics (Calculus Based)/Angular Momentum and its Conservation

Course Title: Calculus Based Physics I

Lecture Topic: Angular Momentum and its Conservation

Instructor: Liang Zeng

Institution: University of Texas-Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Know the definition for angular momentum L ⃗=r ⃗ ×p ⃗=r ⃗  ×mv ⃗ (direction, right-hand rule) for a particle
 * Know how to calculate angular momentum for multi-particle system  L ⃗=∑▒  r ⃗_i  ×m_i v ⃗_i
 * Know why we need and how to calculate moment of inertia for rigid bodies (continuous mass distribution): L ⃗=Iω ⃗   where  I= ∑▒〖m_i r_i^2 〗   becomes the integration of r2 with regard to dm; how to determine the direction of angular momentum (right-hand rule)
 * Know the formula for moment of inertia and its values for rigid objects of the most common shapes: rod, cylinder, ball, thin-shell type, plate
 * Know that torque equals change of angular momentum, definition of torque  τ ⃗=r ⃗  ×F ⃗, relate this to physical problems; determine the direction of τ ⃗ (right-hand rule)
 * Know how to geometrically determine center of mass in order to calculate the magnitude of position vector r ⃗ in the torque formula
 * Know how to calculate center of mass for more complicated shapes based on calculus (line density, area density, etc.)
 * Know the relation τ ⃗=(dL ⃗)/dt=d(Iω ⃗ )/dt=I × α ⃗   ( assume I is constant); α ⃗ is related to the change of angular speed
 * Know the relationship between α ⃗ and tangential acceleration: a ⃗= α ⃗r
 * Know when the law of Conservation of Angular Momentum applies (when net torque = 0)
 * Discern in the some physical systems whether net torque equals or is not equal to 0 (revolution of planets around the Sun in solar system, neutron star spinning faster when it collapses, etc.)
 * Know when net torque does not equal 0, total angular momentum does not conserve, consequently, change of angular momentum: phenomena such as a spinning wheel falling down, precession, a spinning wheel stabilize itself better than a non-spinning wheel, a fast-moving bicycle is not as easy to fall as a slow-moving bicycle
 * When net torque is not equal to 0, a spinning object will undergo precession (earth, gyroscope, top)

 * Sub Objectives- The objectives will require that students be able to:
 * text
 * text

 * Difficulties- Students may have difficulty:
 * Calculating center of mass and moment of inertia using calculus
 * Determining the directions of angular momentum and torque using right-hand rule
 * Determining the direction of torque in seesaw (non-intuitive)
 * Why we use the right hand rule to determine the direction of torque - counter-clockwise, clockwise depends on observer’s position, more ambiguous
 * Understanding why net torque can change angular momentum
 * Understanding why we need to introduce angular momentum
 * In rotation (m,r ⃗,ω ⃗) using an example opening a door: your hand pushing at the knob versus pushing in the middle
 * Earth spinning: somebody standing on the equator versus at another altitude, r and v are both changing, but omega is the same (one circle per 24 hours)
 * Compare linear momentum (kg m/s) with angular momentum (rotational/circular momentum) ( kg m2/s) – units are different
 * Terms: circular (of a circle), rotational (of rotation), and angular (of angle) momentum mean pretty much the same, different emphasis
 * When a person walks toward center of the merry-go-around or visa versa, r changes, v changes, moment of inertia changes between the initial and final positions
 * Determining when net torque equals zero: Earth revolution example
 * Net torque of earth’s revolution around the Sun:  τ ⃗=r ⃗  ×F ⃗=0  (r is parallel to F, so τ ⃗ = 0, so the law of conservation of angular momentum applies). More understanding of Kepler’s second law: Earth covers same area between the Sun and the earth revolution orbit per unit time. Area is a function of angular momentum and time span
 * Conservation of angular momentum but not angular acceleration: LEarth is constant, L = mvr = mωrr = mr2ω but r is changing with t, so I = mr(t)2 is changing, then ω(t) is changing.  There is an angular acceleration as a function of time, and earth revolves faster nearer the sun than farther away

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Gyroscope applications: orientation in Gravity Probe 2; Tedco Toy Gyroscope – from gyroscope.com*
 * Fly wheel on a boat (insert boat models and specifications), NASA fly wheel picture*
 * A faster spinning wheel has a larger angular momentum and requires a larger torque to affect it, compared to a slower spinning wheel (with a smaller angular momentum), so a faster spinning wheel is more stable. Example: riding a bike quickly versus riding a bike slowly.
 * Analyze speed of earth when it moves near the Sun and farther away from the Sun (speed and distance data: nearest, farthest positions); conservation of angular momentum (m1v1r1=m2v2r2) ω is not the same   m1 = m2    r1 > r2     v1 < v2
 * Ice skaters and divers – body positioning and arm/hand positioning affects angular speed (needs more research and specification on positioning – try to get a video for slow-motion view of ice skaters and divers)*
 * Spinning of yo-yo – angular momentum – play the Toys in Space video clip, use text reference (Wilson)*
 * Astrojax – string with two balls secured at each end of the string and one free to move along the length of the string. Play the Toys in Space video clip*

Model of Knowledge

 * Concept Map
 * text
 * text
 * text

 * Content Priorities
 * Enduring Understanding
 * Definition for angular momentum for a particle;direction of angular momentum (right-hand rule)
 * Calculate angular momentum for multi-particle system
 * Calculate moment of inertia for rigid bodies (continuous mass distribution)
 * Formula for moment of inertia and it values for rigid objects of most common shapes : rod, cylinder, ball, thin-shell type, plate
 * Torque equals change of angular momentum, definition of torque and determine direction (right-hand rule)
 * Calculate net torque
 * Geometrically determine center of mass for very simple shapes in order to calculate the magnitude of position vector in torque formula
 * Calculate center of mass for more complicated shapes based on calculus (line density, area density, etc.)
 * Angular acceleration α→ = a→/r
 * When the law of Conservation of Angular Momentum applies (when net torque = 0)
 * Whether net torque equals or not equal to 0 in some physical systems (all planets revolution around the Sun in solar system, neutron star spinning faster when it collapses, etc.)
 * Stabilization: A faster spinning wheel has a larger angular momentum and requires a larger torque to affect it, compared to a slower spinning wheel (with a smaller angular momentum), so a faster spinning wheel is more stable. Example: riding a bike quickly versus riding a bike slowly.
 * Important to Do and Know
 * Calculate moment of inertia for most common shaped rigid objects: rods, plates, sphere, thin-wall sphere, cylinder, thin-wall cylinder
 * How gyroscopes work
 * Precession: when torque does not equal 0, total angular momentum does not conserve, consequently, change of angular momentum: a spinning object with nonzero net torque will undergo precession (earth, gyroscope, top). Direction of angular momentum follows direction of torque.
 * Worth Being Familiar with
 * Center of mass
 * When applying a lifting force on one handle of the axis of the spinning wheel, determine net torque, describe your feeling about the immediate behavior of the spinning wheel and why
 * Earth's revolution around the sun: conservation of angular momentum but not angular acceleration: LEarth is constant, L = mvr = mωrr = mr2ω but r is changing with t, so I = mr(t)2 is changing, then ω(t) is changing.  There is an angular acceleration as a function of time

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * text
 * text
 * Homework (individual)
 * text
 * text
 * Summative Assessment
 * text
 * text

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * text
 * text
 * text
 * text
 * text
 * text

THE CHALLENGE

Format: 1. Put down your name. 2. State challenge question and its number. 3. Show all your work.
 * Instructions: students can refer to any resource to answer this question. Each person needs to scan and save the report as a pdf file, and email the report to Mr. Manuel Lara, Teaching Assistant on WebCT which answers the question with supporting data linking back with the relevant physics content. The report is usually due a week from the date when the question is assigned and will be kept in a WebCT folder.
 * Rubric for grades (on a 0-10 point scale): 1. Correct solution for the amount of tension and the contributions to the overall torque before the rope is burned (4 points). 2. Correct solution for the contributions to the overall torque after the rope is burned (3 points). 3. Correct solution for the direction of precession of the wheel (3 points).

Challenge Question #6: Watch the Youtube video: “Do Try This At Home: Episode 7 – The Wheel”. Two looped ropes are hanging from a beam and a wheel is placed between the two ropes. The wheel is given a spin and one of the ropes is burned so that it no longer supports the wheel. The wheel does not fall, but continues to spin and begins precessing.

a) Analyze using variables the amount of tension in each rope and the various contributions to the overall torque before the rope is burned.

b) Analyze using variables the various contributions to the overall torque in the system after the rope is burned.

c) Analzye why the wheel precesses in the direction that it does in the video after the rope is burned.

GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Pre-Lesson Quiz

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Test Your Mettle Quiz
1. (Moment of inertia in a multi particle system: Knight 2nd edition page 378 #14). The four masses shown in the figure are connected by massless, rigid rods (the lines extending horizontally to the right of D and vertically above B are to indicate an xy coordinate system).

a)Find the coordinates of the center of mass b)Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page.

2. (Moment of inertia for a rigid body: Knight 2nd edition page 381 #56). Determine the moment of inertia about t5he axis of the object shown in the following figure.

3. (Angular momentum for a single particle: Knight 2nd edition page 380 #46). What are the magnitude and direction of the angular momentum relative to the origin of the 200 g particle in the following figure.

4. (Angular momentum for a multi particle system: Serway 7th edition page 330 #11). A light, rigid rod 100 m in length joins two particles, with masses 4.00 kg and 3.00 kg, at its ends. The combination rotates in the xy plane about a pivot through the center of the rod (see figure below). Determine the angular momentum of the system about the origin when the speed of each particle is 5.00 m/s.

5. (Net torque: Serway 7th edition page 302-303 #33). Find the net torque on the wheel in the following figure about the axle through O, taking a = 10.0 cm and b = 25.0 cm.

6. (Practice on mvr variables: Serway 7th edition page 332 #32a). A student sits on a freely rotating stool holding two dumbbells, each of mass 3.00 kg (see figure below). When the student’s arms are extended horizontally (figure a), the dumbbells are 1.00 m from the axis of rotation and the student rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool is 3.00 kg•m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.300 m from the rotation axis (figure b). Find the new angular speed of the student.

7. (Conservation of angular momentum: Knight 2nd edition page 383 #81). A satellite follows the elliptical orbit shown. The only force on the satellite is the gravitational attraction of the planet. The satellite’s speed at point a is 8000 m/s.

a)Is there any torque on the satellite? Explain. b)What is the satellite’s speed at point b? c)What is the satellite’s speed at point c?

8. (Torque and change of angular momentum: Serway 7th edition page 304 #49). This problem describes one experimental method for determining the moment of inertia of an irregularly shaped object such as the payload for a satellite. The figure below shows a counterweight of mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. The turntable can rotate without friction. When the counterweight is released from rest, it descends through a distance h, acquiring a speed v. Show that the moment of inertia I of the rotating apparatus (including the turntable) is mr2(2gh/v2 – 1).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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UTPA STEM/CBI Courses/Physics (Calculus Based)/Work Energy Theorem and the Conservation of Energy

θCourse Title: Calculus Based Physics I

Lecture Topic: Work Energy Theorem and the Conservation of Energy

Instructor: Dr. Linag Zeng

Institution: University of Texas-Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Know the definition for rotational energy and how to calculate rotational energy for a single particle
 * Know the definition for rotational energy and how to calculate rotational energy for a rigid body
 * Review kinetic energy
 * Know the definition for potential energy and how to calculate potential energy
 * Know the definition of work and how to calculate work using the dot product
 * Know that the amount of work done by conservative forces (eg. gravity) or restorative forces (eg. spring) does not depend on the path; the amount of work done by non-conservative forces (eg. friction)  does depend on the path
 * Know the relationship between work and energy – work is not a form of energy (although it has units of Joules), but work can produce or consume energy
 * Know the definition for spring potential energy and how to calculate spring potential energy (Hook’s Law)
 * Know the definition of the system - anything included in an area/volume within a boundary (examples cell, tree bark, skin on body, ecosystem, sun). Know how to identify the system from reading the question. Know how to determine if the system is isolated or not isolated from the surroundings (isolated means that there is no energy exchange across the boundary).
 * Know that most situations in this course are isolated systems. Know how to identify the conservative and non-conservative forces in the system. If all the forces in the system are conservative then conservation of mechanical energy can be applied. If at least one of the forces is non-conservative then the work-energy theorem (net work = change of total energy) must be used.
 * Know different forms of energy transfer where energy is not conserved for a system (sound, electrical, electromagnetic radiation, matter transfer, mechanical waves, heat).
 * Know definition of power: the change of energy over time, or the change of work over time. Know the unit of power: Watt. Know that your electrical bill comes in units of energy (kW x hour).

 * Sub Objectives- The objectives will require that students be able to:
 * text
 * text

 * Difficulties- Students may have difficulty:
 * Using Hook's Law:F→ = -kx→ a)Understanding why there is a negative sign: F→ and x→ are proportional but in opposite directions
 * Identifying properties of a system: isolated versus non-isolated
 * Identifying conservative forces versus non-conservative forces
 * When to apply conservation of mechanical energy (conservative forces) versus when to apply the work-energy theorem (at least one non-conservative force)
 * Identifying the different forms of energy to be considered in the initial state versus the final state
 * Understanding that work and energy are both scalar quantities, but signs for work are inherited from the formulas used to calculate work depending on the angle between the force and displacement involved, while the signs for change of energy depend on the difference (subtraction) of initial from final energy (W = ΔE = Ef – Ei).

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * The use of a ramp to push an object onto the back of a truck versus lifting it yourself. The total work is the same, but with the ramp the distance is longer so the force is smaller*
 * Waterfalls, skiing, and hydroelectric plants at dams – conversion of potential energy to kinetic energy (and then mechanical and electrical energy) from the top of the waterfall to the bottom of the waterfall*
 * Music boxes – wind the spring to create potential energy then the potential energy is converted to other forms of energy to play music or make the figurine twirl etc.
 * Car shock absorber springs in the tires – when the car runs over something there is not much bouncing because the spring constant (F = -kx) is very large resulting in a small displacement*
 * Car engine: battery has chemical energy converted to electrical energy, causes a spark which ignites the fuel so chemical potential is converted to heat energy, heat expands air which causes pistons to move up and down so heat energy is converted to mechanical energy, pistons are connected to rods and gears which cause the tires to turn*
 * Solar energy from the sun is used by plants to grow and people eat plants for energy and then can do work. Continue with discussion from students*

Model of Knowledge

 * Concept Map
 * text
 * text
 * text

 * Content Priorities
 * Enduring Understanding
 * Definition for rotational energy and calculate rotational energy for a single particle
 * Definition for rotational energy and calculate rotational energy for a rigid body, including a rotational pulley example
 * Review kinetic energy
 * Definition for potential energy and calculate potential energy
 * Definition of work and calculate work (W = F→ · d→) using the dot product
 * Amount of work done by conservative forces (eg. gravity) or restorative forces (eg. spring) does not depend on the path; the amount of work done by non-conservative forces (eg. friction)  does depend on the path
 * Relationship between work and energy – work is not a form of energy (although it has units of Joules), but work can produce or consume energy
 * Definition for spring potential energy and calculate spring potential energy (Hook’s Law)
 * Definition of the system - anything included in an area/volume within a boundary. (Give lots of examples – cell, tree bark, skin on body, ecosystem, sun). Identify the system from reading the question. Determine if the system is isolated or not isolated from the surroundings (isolated means that there is no energy exchange across the boundary).
 * Most situations in this course are isolated systems. Identify the conservative and non-conservative forces in the system. If all the forces in the system are conservative then conservation of mechanical energy can be applied. If at least one of the forces is non-conservative then the work-energy theorem (work = change of energy) must be used
 * Definition of power: the change of energy over time, or the change of work over time (force * velocity). Know the unit of power: Watt. Electric bill comes in units of energy (kW x hour)
 * Important to Do and Know
 * Different forms of energy transfer where energy is not conserved for a system (sound, electrical, electromagnetic radiation, matter transfer, mechanical waves, heat)
 * Worth Being Familiar with
 * In other systems there are other forms of transfer of energy – matter transfer, electrical transmission, electromagnetic radiation
 * Faraday's universal conservation of energy hypothesis (total energy in the universe is conserved – Physics Today)

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * text
 * text
 * Homework (individual)
 * text
 * text
 * Summative Assessment
 * text
 * text

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * text
 * text
 * text
 * text
 * text
 * text

THE CHALLENGE

Rubric for grades (on a 0-10 point scale): 1. Correct solution for the speed the driver was going when he got onto the ramp (8 points). 2. Reasonable recommendation to avoid similar accidents at this overpass (2 points). Format: 1. Put down your name. 2. State challenge question and its number. 3. Show all your work.
 * Instructions: students can refer to any resource to answer this question. Each person needs to scan and save the report as a pdf file, and email the report to Mr. Manuel Lara, Teaching Assistant on WebCT which answers the question with supporting data linking back with the relevant physics content. The report is usually due a week from the date when the question is assigned and will be kept in a WebCT folder.

Challenge Question #7: The westbound lanes of Expresseway 83 in McAllen have an exit leading to a ramp that leads to an overpass along Bicentennial Boulevard that you can use to get to the Miller International Airport. The ramp goes up and ends in a T-junction which merges onto Bicentennial Boulevard (see figures). Several accidents have occurred at this T-junction because drivers coming up the ramp are not able to successfully make the turn at the T-junction, and going forward through the T-junction results in you going through a barrier, dropping off the overpass and landing on the Expresseway 83 below. A driver recently had an accident at the T-junction, where he hit the barrier at the T-junction causing the bumper on the front of his car to be compressed by 1 foot (the bumper collision can be approximated as a spring with a spring constant k = 150 N/m). The width of the T-junction from the end of the ramp to the barrier is 20 feet, and coefficient of friction between the asphalt surface and the car tires when the vehicle is braking is 0.7 (it was a foggy day). The height of the overpass is 18.5 feet above the Expresseway, and the horizontal distance from the beginning of the ramp to the beginning of the T-junction is 115 feet (the rolling friction is .015). There were faint and alternating skid marks across the entire 20 feet span of the T-junction, indicating that the driver slammed on his brakes across the entire span of the T-junction. The driver reported that once he left the Expresseway and got onto the ramp he took his foot off the accelerator and did not hit the brakes until he got to the T-junction. The speed limit for the ramp was 45 mph. How fast was the driver going when he got onto the ramp? Based on your calculation of the velocity, what would you recommend to avoid similar accidents at this overpass? Justify your answer.

GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

text

Pre-Lesson Quiz

 * 1) question
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Test Your Mettle Quiz
1. (Rotational energy for a rigid body: Serway 7th edition page 332 #32b). A student sits on a freely rotating stool holding two dumbbells, each of mass 3.00 kg (see figure). When the student’s arms are extended horizontally (figure a), the dumbbells are 1.00 m from the axis of rotation and the student rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool 3.00 kg•m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.300 m from the rotation axis (figure b). Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward.

2. (Free fall: Shipman, Wilson, and Todd, 12th edition page 98 #17). An object is dropped from a height of 12 m. At what height will its kinetic energy and its potential energy be equal?

3. (Potential and kinetic energy irregular slide: Serway 7th edition page 218 #4). A particle of mass m = 5.00 kg is released from point A and slides on the frictionless track shown in the figure. Determine the following:

a)The particle’s speed at points B and C b)The net work done by the gravitational force as the particle moves from A to C

4. (Work with a force applied at an angle to displacement: Serway 7th edition page 189 #1). A block of mass 2.50 kg is pushed 2.20 m along a frictionless horizontal table by a constant 16.0-N force directed 25° below the horizontal.

a)Determine the work done on the block by the applied force b)Determine the work done on the block by the normal force exerted by the table c)Determine the work done on the block by the gravitational force d)Determine the net work done on the block

5. (Conservative force: Serway 7th edition page 192 #39). A 4.00-kg particle moves from the origin to position C, having coordinates x = 5.00 m and y = 5.00 m (see figure). One force on the particle is the gravitational force acting in the negative y direction. Using equation 7.3 from your textbook, calculate the work done by the gravitational force on the particle as it goes:

a) From O to C along OAC b) From O to C along OBC c) From O to C along OC d) Your results should all be identical. Why?

6. (Non-conservative force: adapted from Serway 7th edition page 192 #39). The same 4.00-kg particle from the previous question moves from the origin to position C, having coordinates x = 5.00 m and y = 5.00 m (see figure). Another force on the particle is a friction force with magnitude 3.00 N and acting in the direction opposite to the particle’s displacement. Calculate the work done by the friction force on the particle as it moves along the following paths:

a)OAC b)OBC c)OC d)Are all of your results identical? If not, why?

7. (Relationship between work and energy: Walker 2nd edition page 194 #22). A 1300-kg car coasts on a horizontal road with a speed of 18 m/s. After crossing an unpaved, sandy stretch of road 30.0 m long its speed decreases to 15 m/s.

a)Was the net work done on the car positive, negative, or zero? Explain. b)Find the magnitude of the average net force on the car in the sandy section.

8. (Spring potential and object kinetic energy: Serway 7th edition page 193 #57). The ball launcher in a pinball machine has a spring that has a force constant of 1.20 N/cm (see figure). The surface on which the ball moves is inclined 10.0° with respect to the horizontal. The spring is initially compressed 5.00 cm. Find the launching speed of a 100-g ball when the plunger is released. Friction and the mass of the plunger are negligible.

9. (Pulley, no mass or rotation of pulley: Serway 7th edition page 219 #7). Two objects are connected by a light spring passing over a light, frictionless pulley as shown in the figure. The object of mass 5.00 kg is released from rest. Using the isolated system model:

a)Determine the speed of the 3.00-kg object just as the 5.00-kg object hits the ground. b)Find the maximum height to which the 3.00-kg object rises.

10. (Pulley, with mass and rotation of pulley: Serway 7th edition page 304 #44). Consider the system shown in the figure with m1 = 20.0 kg, m2 = 12.5 kg, R = 0.200 m, and the mass of the uniform pulley M = 5.00 kg. Object m2 is resting on the floor, and object m1 is is 4.00 m above the floor when it is released from rest. The pulley axis is frictionless. The cord is light, does not stretch, and does not slip on the pulley. Calculate the final velocity of m1 when it is about to hit the floor.

11. (Conservation of mechanical energy and projectile motion: Walker 2nd edition page 230 #57). The water slide shown in the figure (scan and insert figure) ends at a height of 1.50 m above the pool. If the person starts from rest at point A and lands in the water at point B, what is the height h of the water slide? (Assume the water slide is frictionless).

12. (Pendulum-like question: Serway 7th edition page 264 #47a and 47b). A particle is suspended from a post on top of a cart by a light string of length L as shown in the figure (figure a). The cart and particle are initially moving to the right at constant speed vi with the string vertical. The cart suddenly comes to rest when it runs into and sticks to a bumper as shown in the figure (figure b). The suspended particle swings through an angle.

a)Show that the original speed of the cart can be computed from vi = (2gL(1-cosθ))^1/2 b)Find the initial speed implied by L = 1.20 m and  = 35.0°.

13. (Power in a moving elevator: Serway 7th edition page 221 #32). A 650-kg elevator starts from rest. It moves upward for 3.00 s with constant acceleration until it reaches its cruising speed of 1.75 m/s.

a)What is the average power of the elevator motor during this time interval? b)How does this power compare with the motor power when the elevator moves at its cruising speed?


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UTPA STEM/CBI Courses/Physics (Calculus Based)/Universal Gravitational Force

Course Title: Calculus Based Physics I

Lecture Topic: Universal Gravitational Force

Instructor: Feng

Institution: University of Texas-Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Know that the universal gravitational force applies to any object that has mass
 * Know how to calculate the magnitude of the universal gravitational force (G = 6.67 x 10-11 Nm2kg-2) F = Gm1m2/r122
 * r can be taken to be (altitude + radius of earth) for problems considering space objects
 * Weight mg comes from using the universal gravitational force formula where m2 is the mass of earth and r12 is the radius of earth, m1 is the person’s mass standing on earth’s surface, and g = Gm2/r122 = 9.8 m/s2
 * Know how to discern when the gravitational force has no noticeable effect and is negligible (between two people the gravitational force is not noticeable because the masses are not heavy enough and G is so small; between planets/sun the gravitational force is noticeable)
 * Know that in subatomic particle (electrons, protons) the Coulomb force (introduce formula for Coulomb force) is dominant over the gravitational force
 * Know the gravitational potential energy formula and how to apply it
 * Know how to find escape speed from the earth versus from the moon (also show list of escape speeds from other planets)
 * Know the statements of Kepler’s three laws and how to derive and apply Kepler’s third law

 * Sub Objectives- The objectives will require that students be able to:
 * text
 * text

 * Difficulties- Students may have difficulty:
 * Units of the universal gravitational force constant G (Nm2/kg2)
 * Students tend to forget to square r when calculating gravitational force
 * At an altitude h to calculate the gravitational force the denominator must be (rearth + h)2
 * Negative sign in gravitational potential energy formula (negative sign indicates force is attractive)
 * Assuming that rmax goes to infinity when deriving escape speed.

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as: (* = picture/video/data in Supplementary Materials in Blackboard):
 * The gravitational force formula applies to all bodies with mass in the universe.
 * Satellites in circular motion about the earth: The relation between orbital radius and period, T2 proportional to r3 (Calculate T2/r3 using data from http://www.freemars.org/jeff/speed/index.htm, create Excel file using data)*
 * Planetary motion about the sun: Kepler’s laws, Table 13.2*
 * Satellite leaving solar system must be traveling at or about the escape velocity for the solar system (get some data for satellite, explain why it was able to leave solar system)*
 * Solar wind leaves the sun with extreme speeds in order to escape the sun gravitational force (get some data on solar winds, compare with escape speed 617.5 km/s, sun’s escape speed, discussion on consequence of solar wind on earth magnetic field and comet tail)*
 * Weight of objects on different planets, (astronauts walking on the moon)
 * Tidal effects due to the gravitational pull of the moon and sun
 * Identifying planets around distant stars by observing wobbles or slight deviation from calculated orbit of the distant stars*
 * Saturn’s ring
 * Ability to send objects to other planets: Sling shot (Voyager)*

Model of Knowledge

 * Concept Map
 * text
 * text
 * text

 * Content Priorities
 * Enduring Understanding
 * Calculate the magnitude of the universal gravitational force (G = 6.67 x 10-11 Nm2kg-2) F = Gm1m2/r122
 * Know that the universal gravitational force applies to any object that has mass
 * r can be taken to be (altitude + radius of earth) for problems considering space objects
 * Weight mg comes from using the universal gravitational force formula where m2 is the mass of earth and r12 is the radius of earth, m1 is the person’s mass standing on earth’s surface, and g = Gm2/r122 = 9.8 m/s2
 * Contrast: discern when the gravitational force has no noticeable effect and is negligible (between two people the gravitational force is not noticeable because the masses are not heavy enough and G is so small; between planets/sun the gravitational force is noticeable)
 * Gravitational potential energy formula and how to apply it
 * Derive and apply escape speed for Earth
 * Statements of Kepler’s three laws and derivation and application of Kepler’s third law
 * Important to Do and Know
 * Contrast: in subatomic particle (electrons, protons) the Coulomb force (introduce formula for Coulomb force) is dominant over the gravitational force
 * Derive and apply escape speed for different planets or celestial objects
 * Worth Being Familiar with
 * Understand in some detail Keplers 1st and 2nd law (supplemental material link)

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * text
 * text
 * Homework (individual)
 * Pay attention to the following new units: G Gravitational force constant(N m2/kg2), K Coulomb force constant (N m2/C2)
 * Self-reading Sections Chapter 13 in the textbook
 * Summative Assessment
 * text
 * text

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * text
 * text
 * text
 * text
 * text
 * text

THE CHALLENGE

Instructions: Students can refer to any resource to answer this question. Each person needs to scan and save the report as a pdf file, and email the report to Mr. Manuel Lara, Teaching Assistant on WebCT which answers the question with supporting data linking back with the relevant physics content. The report is usually due a week from the date when the question is assigned and will be kept in a WebCT folder.

Rubric for grades (on a 0-10 point scale):
 * 1) Correct algebraic set-up to begin the solution (3 points)
 * 2) Algebraic manipulation (3 points)
 * 3) Correct solution of SOHO’s distance from earth (4 points).

Format:
 * 1) Put down your name
 * 2) State challenge question and its number
 * 3) Show all your work.

Challenge Question #8: (Knight 2nd edition). In 1996, the Solar and Heliospheric Observatory (SOHO) was “parked” in an orbit slightly inside the earth’s orbit, as shown in the figure (scan and insert figure). The satellite’s period in this orbit is exactly one year, so it remains fixed relative to the earth. At this point, called a Lagrange point, the light from the sun is never blocked by the earth, yet the satellite remains “nearby” so that data are easily transmitted to earth. What is SOHO’s distance from the earth? (Useful parameters: mass of the sun = 1.991 x 1030 kg, mass of earth = 5.983 x 1024 kg, distance from the sun to earth = 1.496 x 1011 m, 1.000 year = 3.156 x 107 s). Hint: your final algebraic equation will contain powers of the variable ranging from the fifth to the zeroth, so do not try to solve the equation algebraically – you may use computer software such as Excel, MatLab, Mathematica, Maple, graphing calculator, etc.

GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Pre-Lesson Quiz

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Test Your Mettle Quiz

 * 1) (Universal gravitational force law: Serway 7th edition page 381 #6i). A satellite originally moves in a circular orbit of radius R around the Earth. Suppose it moved into a circular orbit of radius 4R. What does the force exerted on the satellite then become?
 * a. 16 times larger
 * b. 8 times larger
 * c. 4 times larger
 * d. 2 times larger
 * e. unchanged
 * f. 1/2 as large
 * g. 1/4 as larger
 * h. 1/8 as large
 * i. 1/16 as large
 * 1) (Gravitational force between two arbitrary masses: Serway 7th edition page 382 P#1). Determine the order of magnitude of the gravitational force that you exert on another person 2 m away. In your solution, state the quantities you measure or estimate and their values.
 * 2) (Gravitational force at some altitude above earth: online resource “Geostationary Satellite Problem”). A 2100 kg satellite is to be placed into a circular, geostationary orbit above the equator. How high above the equator will the satellite have to be in orbit in order for it to be stationary above one location on the equator.
 * 3) (Gravitational acceleration on a different planet or moon: Serway 7th edition page 381 #5). Suppose the gravitational acceleration at the surface of a certain satellite A of Jupiter is 2 m/s2. Satellite B has twice the mass and twice the radius of satellite A. What is the gravitational acceleration at its surface?
 * a. 16 m/s2
 * b. 8 m/s2
 * c. 4 m/s2
 * d. 2 m/s2
 * e. 1 m/s2
 * f. 0.5 m/s2
 * g. 0.25 m/s2
 * 1) (Gravitational potential energy difference at different altitudes: Serway 7th edition page 385 #32). A 1000-kg satellite orbits the Earth at a constant altitude of 100 km. How much energy must be added to the system to move the satellite into a circular orbit with altitude 200 km? Discuss the changes in kinetic energy, potential energy, and total energy.
 * 2) (Escape velocity: Serway 7th edition page 385 #30a). What is the minimum speed, relative to the Sun, necessary for a spacecraft to escape the solar system, if it starts at the earth’s orbit?
 * 3) (Kepler’s laws: Serway 7th edition page 384 #15). Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22 x 105 km. From these data, determine the mass of Jupiter.


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UTPA STEM/CBI Courses/Physics (Calculus Based)/Static Equilibrium and Elasticity

Course Title: Calculus Based Physics I

Lecture Topic: Static Equilibrium and Elasticity

Instructor: Dr. Zeng

Institution: University of Texas-Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Know the conditions for equilibrium (net force = 0, net torque = 0)
 * Know what we mean by a system being in static equilibrium (v=0)
 * Analyze forces in x and y directions for a 2-D system, free body diagram
 * Review center of mass and how it relates to gravitational forces on objects like beams (uniform density)
 * Analyze the net torque for a system
 * Know how to analyze systems where there are forces and torques acting on the system
 * Know how to analyze elastic properties of solids (Young’s modulus, shear modulus, bulk modulus)

 * Sub Objectives- The objectives will require that students be able to:
 * text
 * text

 * Difficulties- Students may have difficulty:
 * Selecting the proper coordinate systems for a given problem, forces
 * Identifying all the acting forces and the respective directions of the forces; forces should point away from object (tension along cord, direction of friction opposite to the direction of impending motion, and normal forces perpendicular to the surface)
 * Selecting a proper pivot point and calculating net torque
 * Identifying the proper signs for torque

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Balances: Triple beam balance*
 * Bridges: Golden Gate Bridge, Queen Isabel Bridge
 * Different types of trusses (roofs, towers, bridges, cranes): Lattice Truss, Pratt Truss (http://en.wikipedia.org/wiki/Truss)*
 * Building structure: House frame, building frame*
 * Ballerinas, skaters, skateboarders, gymnasts, and other athletes : Must be aware of their center of mass to better balance their self
 * Support cables on electric posts*
 * Cantilever beams*
 * Unicycle*
 * Stilts*
 * Human pyramids, building a house of cards*

Model of Knowledge

 * Concept Map
 * text
 * text
 * text

 * Content Priorities
 * Enduring Understanding
 * Static equilibrium refers to an object at rest and satisfies two necessary conditions: net force = 0, net torque = 0)
 * Draw free body diagrams to analyze forces in the x and y directions in a 2-D system
 * The balancing force for the weight in a 2-D system must go through the center of mass (review the calculation of center of mass)
 * Analyze the net torque for a system
 * Know how to analyze systems where there are forces and torques acting on the system: how to select a pivot point, how to determine the direction of forces, how to identify all the acting forces
 * Know how to do basic calculations for Young’s modulus, shear modulus, and bulk modulus
 * Important to Do and Know
 * Know when a system is in equilibrium, v = 0 or v = constant
 * Determination of the tensile stress and breaking point of a material using stress-strain curves for elastic solids (Figure 12.13 Serway 7th edition page 348)

 * Worth Being Familiar with
 * Comparison of properties of materials (Young’s modulus, shear modulus, and bulk modulus, yield point), Table 12.1 page 348 in Serway 7th edition
 * Analysis of forces acting on free body diagrams in three dimensions

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * text
 * text
 * Homework (individual)
 * Pay attention to the following new units: N/m2 (Young’s modulus, shear modulus, bulk modulus)
 * Self-reading Chapter 12 in the textbook

 * Summative Assessment
 * text
 * text

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * text
 * text
 * text
 * text
 * text
 * text

THE CHALLENGE

Observe the electric poles in the following pictures – they were all taken from areas in or surrounding UTPA. Use free body diagrams to analyze all the forces present acting on each of the poles in the pictures. Justify why the support cables (metal cable(s) going from the upper half of the pole to the ground) are necessary. Make sure to go outside and look at these electric poles or other similar electric poles. Instructions: students can refer to any resource to answer this question. Each person needs to scan and save the report as a pdf file, and email the report to Mr. Manuel Lara, Teaching Assistant on WebCT which answers the question with supporting data linking back with the relevant physics content. The report is usually due a week from the date when the question is assigned and will be kept in a WebCT folder. Rubric for grades (on a 0-10 point scale): 1. Correct free body diagram and analysis of forces for picture a (5 points). 2. Correct free body diagram and analysis of forces for picture b (5 points). Format: 1. Put down your name. 2. State challenge question and its number. 3. Show all your work.
 * Challenge question for the students (10 points each, 10% for 12 modules):

 * a) Southeast corner of the intersection of Van Week Street and Sugar Road.

 * b) Northeast corner of the intersection of Sugar Road and University Drive.

GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Pre-Lesson Quiz

 * 1.	(Static equilibrium sum of forces = 0, sum of torque = 0, cantilever: Serway 7th edition page 357 #37). A hungry bear weighing 700 N walks out on a beam in an attempt to retrieve a basket of food hanging at the end of the beam (see figure). The beam is uniform, weighs 200 N, and is 6.00 m long; the basket weighs 80.0 N.
 * a.	Draw a free-body diagram for the beam.
 * b.	When the bear is at x = 1.00 m, find the tension in the wire and the components of the force exerted by the wall on the left end of the beam.
 * c.	If the wire can withstand a maximum tension of 900 N, what is the maximum distance the bear can walk before the wire breaks?
 * 2.	(Static equilibrium sum of forces = 0, sum of torque = 0, fish on scale: Serway 7th edition page 358 #43). A 10 000-N shark is supported by a cable attached to a 4.00 m rod that can pivot at the base. Calculate the tension in the tie rope between the rod and the wall, assuming the tie rope is holding the system in the position shown in the figure. Find the horizontal and vertical forces exerted on the base of the rod. Ignore the weight of the rod.
 * 3.	(Static equilibrium sum of forces = 0, sum of torque = 0, hammer and nail: Serway 7th edition page 355 #10). The figure below shows a claw hammer being used to pull a nail out of a horizontal board. A force of 150 N is exerted horizontally as shown. Assume the force the hammer exerts on the nail is parallel to the nail.
 * a.	Find the force exerted by the hammer claws on the nail.
 * b.	Find the force exerted by the surface on the point of contact with the hammer head.
 * 4.	(Static equilibrium sum of forces = 0, sum of torque = 0, chain: Serway 7th edition page 355 #15). A flexible chain weighing 40.0 N hangs between two hooks located at the same height (see figure). At each hook, the tangent to the chain makes an angle θ = 42.0° with the horizontal.
 * a.	Find the magnitude of the force each hook exerts on the chain.
 * b.	Find the tension in the chain at its midpoint. Suggestion: make a free-body diagram for half of the chain.
 * 5.	(Young’s modulus: Serway 7th edition page 356 #26). A steel wire of diameter 1 mm can support a tension of 0.2 kN. A cable to support a tension of 20 kN should have diameter of what order of magnitude?
 * 6.	(Shear modulus: Serway 7th edition page 356 #27). Assume that if the shear stress in steel exceeds about 4.00 x 108 N/m2, the steel ruptures.
 * a.	Determine the shearing force necessary to shear a steel bolt 1.00 cm in diameter.
 * b.	Determine the shearing force necessary to punch a 1.00-cm-diameter hole in a steel plate 0.500 cm thick.
 * 7.	(Bulk modulus: Serway 7th edition page 357 #29). When water freezes, it expands by about 9%. What pressure increase would occur inside your automobile engine block if the water in it froze? (The bulk modulus of ice is 2.00 x 109 N/m2).

Test Your Mettle Quiz

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UTPA STEM/CBI Courses/Physics (Calculus Based)/Fluid Mechanics

Course Title: Calculus Based Physics I

Lecture Topic: Fluid Mechanics

Instructor: Liang Zeng

Institution: University of Texas-Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Review pressure (P = F/A) – atmospheric pressure, barometer, manometer
 * Know that the term “fluid” includes liquids and gases
 * Know Pascal’s Law (pressure is transmittable in fluids) and its applications
 * Know that pressure increases with depth in fluids (the higher above earth’s surface the lower the pressure, the deeper below the water the greater the pressure) and how to calculate the pressure
 * Know how to calculate buoyant force on an object partially or fully submerged in a fluid; Archimedes principle
 * Know that Av = constant for steady flow rate (volume flux, units of m3/s) through a pipe (so A1v1 = A2v2)
 * Know that the pressure of a fluid decreases as the speed of the fluid increases (Bernoulli) – airplane wings, perfume bottle

 * Sub Objectives- The objectives will require that students be able to:
 * text
 * text

 * Difficulties- Students may have difficulty:
 * Confusion between ρfluid and ρobject when doing calculations involving buoyant objects
 * Confusion between volume of fluid displaced (submerged portion of object) and volume of the entire object
 * Confusion about the point of reference (height versus depth) in the formula P = ρgh

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Snowshoes, high heels, walking upright versus crawling, bed of nails: pressure (P = F/A)*
 * Old-time perfume bottle (Figure 14.23 page 406 Serway), airplane wing and upthrust: Bernoulli’s law*
 * Car brakes, hydraulic lift: Pascal’s law*
 * Three Gorges/Yangzi River, thumb over garden hose: equation of continuity*
 * Iceberg, boat, hot air balloon, floatation devices: buoyancy*

Model of Knowledge

 * Concept Map
 * text
 * text
 * text

 * Content Priorities
 * Enduring Understanding
 * Calculating pressure (P = F/A) – atmospheric pressure, barometer, manometer
 * The term “fluid” includes liquids and gases
 * Pascal’s Law (pressure is transmittable in fluids) and its applications
 * Pressure increases with depth in fluids (the higher above earth’s surface the lower the pressure, the deeper below the water the greater the pressure) and how to calculate the pressure
 * Calculating buoyant force on an object partially or fully submerged in a fluid
 * Av = constant for steady flow rate (volume flux, units of m3/s) through a pipe (so A1v1 = A2v2)
 * Important to Do and Know
 * The pressure of a fluid decreases as the speed of the fluid increases (Bernoulli) – airplane wings, perfume bottle
 * Worth Being Familiar with
 * Calculations using Bernoulli’s equation

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * text
 * text
 * Homework (individual)
 * Pay attention to the following new units: Pa (N/m2), m3, L, kg/m3
 * Self-reading Chapter 14 in the textbook
 * (Calculating pressure using P = F/A, Serway 7th edition #3 page 408). A 50.0 kg woman balances on one heel of a pair of high heeled shoes. If the heel is circular and has a radius of 0.500 cm, what pressure does she exert on the floor?
 * (Pascal’s Law (pressure is transmittable in fluids) and its applications: Hydraulic lift, Serway 7th edition #8 page 409). The small piston of a hydraulic lift has a cross-sectional area of 3.00 cm2 and its large piston has a cross-sectional area of 200 cm2 (figure 14.4a). What force must be applied to the small piston for the lift to raise a load of 15.0 kN? (In service stations, this force is usually exerted by air).

 * (Pressure varies with depth in fluids: Swimming pool no torque, Serway 7th edition #11 page 409). A swimming pool has dimensions 30.0 m x 10.0 m and a flat bottom. When the pool is filled to a depth of 2.00 m with fresh water, what is the force caused by the water on the bottom? On each end? On each side?
 * (Calculating buoyant force on an object: Fully submerged, Serway 7th edition #23 page 411). A 10.0 kg block of metal measuring 12.0 cm x 10.0 cm x 10.0 cm is suspended from a scale immersed in water as shown in Figure P14.22b. The 12.0-cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water.
 * What are the forces acting on the top and bottom of the block? (Take P0 = 101.30 kPa.)
 * What is the reading of the spring scale?
 * Show that the buoyant force equals the difference between the forces at the top and bottom of the block?

 * (Calculating buoyant force on an object: Partially submerged, Serway 7th edition #27 page 411). A cube of wood having an edge dimension of 20.0 cm and a density of 650 kg/m3 floats on water.
 * What is the distance from the horizontal top surface of the cube to the water level?
 * What mass of lead should be placed on the cube so that the top of the cube will be just level with the water?
 * (Flow rate through a pipe is constant (A1v1 = A2v2): hypodermic syringe, Serway 7th edition #49 page 413). A hypodermic syringe contains a medicine having the density of water (Fig. P114.49). The barrel of the syringe has a cross-sectional are A = 2.50 x 10-5 m2, and the needle has a cross-sectional area a = 1.00 x 10-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1 atm. A force F ⃗ of magnitude 2.00 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needles tip.

 * Summative Assessment
 * text
 * text

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * text
 * text
 * text
 * text
 * text
 * text

THE CHALLENGE

text

GENERATE IDEAS

text

MULTIPLE PERSPECTIVES

text

RESEARCH & REVISE

text

TEST YOUR METTLE

text

GO PUBLIC

text

Pre-Lesson Quiz

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UTPA STEM/CBI Courses/Physics (Calculus Based)/Oscillatory Motion

Course Title: Calculus Based Physics I

Lecture Topic: Oscillatory Motion

Instructor: Liang Zeng

Institution: University of Texas-Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Know the definitions of period, frequency, angular frequency (angular frequency is equivalent to angular speed – discussion of artificial unit radians – page 270 Serway)
 * Know how to analyze the motion of an object attached to a horizontal spring in terms of displacement as a function of time
 * Know how to analyze the motion of a pendulum in terms of displacement as a function of time

 * Sub Objectives- The objectives will require that students be able to:
 * text
 * text

 * Difficulties- Students may have difficulty:
 * Understanding the derivation of displacement of a spring/pendulum as a function of time (2nd order differential equation)
 * Understanding that x(t) = Acos(ωt + φ) (equation 15.6 page 420 Serway 7th edition) is representative and not the only way to express displacement; once initial conditions are given various representations are all valid and lead to the same result (eg. sine instead of cosine)
 * Understanding what ω means

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Springs – forces between atoms in solids (page 428 Serway 7th edition)
 * Pendulum – grandfather clock

Model of Knowledge

 * Concept Map
 * text
 * text
 * text

 * Content Priorities
 * Enduring Understanding
 * Definitions of period, frequency, angular frequency (angular frequency is equivalent to angular speed – discussion of artificial unit radians – page 270 Serway)
 * Analyze the motion of an object attached to a horizontal spring in terms of displacement as a function of time
 * Analyze the motion of a pendulum in terms of displacement as a function of time
 * Important to Do and Know
 * Analyze the kinetic and potential energy of simple harmonic oscillators (spring/pendulum) to determine velocity
 * Worth Being Familiar with
 * The physical and torsional pendulums
 * Damped and forced oscillations

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * text
 * text
 * Homework (individual)
 * Pay attention to the following new units: s, Hz, s-1, rads
 * Self-reading Sections Chapter 15: 15.1 – 15.5 (up to the physical pendulum) in the textbook
 * (Motion of simple harmonic oscillator: Serway 7th edition page 441 #6). A simple harmonic oscillator takes 12.0 s to undergo five complete vibrations.
 * Find the period of its motion
 * Find the frequency in hertz
 * Find the angular frequency in radians per second
 * (Energy of simple harmonic oscillator: Serway 7th edition page 442 #17). A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates on a horizontal, frictionless surface with an amplitude of 4.00 cm.
 * Find the total energy of the system when the position is 1.00 cm
 * Find the speed of the object when the position is 1.00 cm
 * Find the kinetic energy when the position is 3.00 cm
 * Find the potential energy when the position is 3.00 cm
 * (Motion of a pendulum: Serway 7th edition page 443 #28 a and b). A simple pendulum is 5.00 m long.
 * What is the period of small oscillations for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2?
 * What is its period if the elevator is accelerating downward at 5.00 m/s2?

 * Summative Assessment
 * text
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Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
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THE CHALLENGE

Astronauts in space need to keep track of their weight as an indicator of their health while living on board the International Space Station. Design an apparatus based on the principles of simple harmonic motion for determining the mass of an astronaut on the International Space Station with zero weight. Give a hand-drawn schematic of the apparatus, describe how it works, and use equations to show how you would determine the mass based on measurable/observable parameters.

GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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UTPA STEM/CBI Courses/Physics (Calculus Based)/Waves and Vibrations

Course Title: Calculus Based Physics I

Lecture Topic: Waves and Vibrations

Instructor: Dr. Liang Zeng

Institution: University of Texas-Pan American

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Know the definition of transverse waves, wavelength, frequency, period, and speed
 * Know the mathematical equation for a wave propagating along the x-direction as a function of time and know the definition of wave number
 * Know that the direction of the wave propagation along the x-direction is reflected in the mathematical equation for wave propagation (-vt and +vt)
 * Know that the speed of sound varies in different media (air, water, glycerol, etc.)
 * Know the mechanism of sound propagation in air, including compression and rarefaction (longitudinal waves)
 * Know the Doppler effect and its applications
 * Know how to determine observed frequency when the source of the sound is moving or the observer is moving (+ and – signs)
 * Know the superposition principle of waves (destructive and constructive interferences)
 * Know the definition and derivation of the wave function of standing waves
 * Know the difference between transverse and longitudinal standing waves
 * Know the definition of resonance and how resonance works
 * Recognize that space distribution and time distribution are separate in the standing wave function, and how the standing wave function compares to the traveling wave
 * Know the characteristics of standing waves (nodes, antinodes, harmonics/modes)
 * Know how to recognize harmonics (1st, 2nd, 3rd, etc.)from diagrams
 * Know the relationship between natural frequency, length, and speed in longitudinal standing waves of sound propagation in a tube

 * Sub Objectives- The objectives will require that students be able to:
 * text
 * text

 * Difficulties- Students may have difficulty:
 * Understanding the signs that differentiate the directions of travelling waves
 * Understanding the signs used in the Doppler effect formula
 * Understanding how the standing wave equation (x and t are in separate terms) is different from the travelling wave equation
 * Recognize harmonic drawings

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Travelling waves: ripples in water, earthquake transverse S waves, earthquake longitudinal P waves, light waves*
 * Transverse standing waves: string instruments, slinky, resonance cavity in lasers*
 * Longitudinal standing waves: wind instruments, drums, convection currents on the sun*
 * Doppler effect: ambulance siren, police car, echocardiogram, ultrasound, Doppler radar for wind speed and direction (page 439 Walker’s book)*
 * Resonance: Tacoma Narrows bridge collapse, standing waves*

Model of Knowledge

 * Concept Map
 * text
 * text
 * text

 * Content Priorities
 * Enduring Understanding
 * Definition of transverse waves, wavelength, frequency, period, and speed
 * Mathematical equation for a wave propagating along the x-direction as a function of time and the definition of wave number
 * The direction of the wave propagation along the x-direction as reflected in the mathematical equation for wave propagation (-vt and +vt)
 * The mechanism of sound propagation in air, including compression and rarefaction (longitudinal waves)
 * Determine observed frequency when the source of the sound is moving or the observer is moving (+ and – signs)
 * The superposition principle of waves (destructive and constructive interferences)
 * The definition of the wave function of standing waves
 * The difference between transverse and longitudinal standing waves
 * The definition of resonance and how resonance works
 * The characteristics of standing waves (nodes, antinodes)
 * The relationship between natural frequency, length, and speed***text
 * Important to Do and Know
 * Know that the speed of sound varies in different media (air, water, glycerol, etc.)
 * The Doppler effect and its applications
 * The derivation of the wave function of standing waves
 * Space distribution and time distribution are separate in the standing wave function, and how the standing wave function compares to the traveling wave
 * Recognize harmonics (1st, 2nd, 3rd, etc.) from standing wave diagrams
 * The relationship between frequency, length, and speed for 2nd and 3rd harmonics
 * Worth Being Familiar with
 * The equation for a simple harmonic oscillator in the vertical direction
 * The formula for wave propagation speed as a function of tension in a string
 * Sound intensity in decibels
 * Frequencies for sonar applications (dolphins, bats, boats)
 * Pressure variation along a tube in sound propagation (page 332 figure 12.11-12 Giancoli, “Physics” 6th edition)

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * In class exercises, flexible to the instructor, for formative assessment
 * Homework (individual)
 * Pay attention to the following new units:
 * Self-reading Chapter 16: 16.1-16.2, 16.4; Chapter 17: 17.1-17.2, 17.4 (up to shock waves); Chapter 18: 18.1-18.5 in the textbook
 * Summative Assessment
 * text
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Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * text
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THE CHALLENGE

Instructions: Students can refer to any resource to answer this question. Each person needs to email the report to Mr. Manuel Lara, Teaching Assistant on WebCT which answers the question with supporting data linking back with the relevant physics content. The report is usually due a week from the date when the question is assigned and will be kept in a WebCT folder.

Rubric for grades (on a 0-10 point scale): Format:
 * 1) List of resources (1 point)
 * 2) Correctly describing the periodic motions (3 points)
 * 3) Correctly describing the factor(s) contributing to the periodic motions and why the periodic motions caused the bridge to collapse (3 points)
 * 4) Making recommendations about how to avoid similar catastrophes (3 points).
 * 1) Put down your name
 * 2) State challenge question and its number
 * 3) Everything has to be typed, font is 12 point time-new roman style
 * 4) The text has to be at least 300 words minimum
 * 5) You can incorporate graphs, figures, tables etc.
 * 6) Save the report as .rtf file.

After viewing the Tacoma Narrows Bridge collapse video (Youtube source, keywords “Tacoma Narrows bridge”), describe the periodic motions of the bridge before it collapses, the factors contributing to the periodic motions, why the periodic motions caused the bridge to collapse, and make recommendations about how to avoid similar catastrophes in future suspension bridges.

GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Test Your Mettle Quiz

 * 1) (Wave propagation as a function of time, positive velocity: Serway 7th edition page 469 #17). A transverse wave on a string is described by the wave function: y=(0.120 m) sin(π/8 x+4πt)
 * 2) Determine the transverse speed and acceleration of the string at t = 0.200 s for the point on the string located at x = 1.60 m
 * 3) What are the wavelength, period, and speed of propagation of this wave?
 * 4) (Wave propagation as a function of time, negative velocity: Serway 7th edition page 469 #13). A sinusoidal wave is described by the wave function: y=(0.25 m)sin(0.30x-40t)where x and y are in meters and t is in seconds.
 * 5) Determine the amplitude for this wave
 * 6) Determine the angular frequency for this wave
 * 7) Determine the angular wave number for this wave
 * 8) Determine the wavelength for this wave
 * 9) Determine the wave speed for this wave
 * 10) Determine the direction of motion for this wave
 * 11) (Doppler effect, source of sound is moving, observer is stationary: Serway 7th edition page 496 #35). Standing at a crosswalk, you hear a frequency of 560 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 480 Hz. Determine the ambulance’s speed from these observations.
 * 12) (Doppler effect, source of sound and observer are moving: Serway 7th edition page 496 #33 a and b). A driver travels northbound on a highway at a speed of 25.0 m/s. A police car, traveling southbound at a speed of 40.0 m/s, approaches with its siren producing sound at a frequency of 2 500 Hz.
 * 13) What frequency does the driver observe as the police car approaches?
 * 14) What frequency does the driver detect after the police car passes him?
 * 15) (Standing waves: Serway 7th edition page 527 #29). Calculate the length of a pipe that has a fundamental frequency of 240 Hz assuming the pipe is
 * 16) closed at one end
 * 17) open at both ends
 * 18) (Resonance: Serway 7th edition page 526 #28). The figure below (part a) (insert figure) is a photograph of a vibrating wine glass. A special technique makes black and white stripes appear where the glass is moving, with closer spacing where the amplitude is larger. Six nodes and six antinodes alternate around the rim of the glass in the vibration photographed, but consider instead the case of a standing-wave vibration with four nodes and four antinodes equally spaced around the 20.0-cm circumference of the rim of a goblet. If transverse waves move around the glass at 900 m/s, an opera singer would have to produce a high harmonic with what frequency to shatter the glass with a resonant vibration as shown in the figure (part b)?
 * 19) (Natural frequency, length, and speed: Serway 7th edition page 527 #36). A tunnel under a river is 2.00 km long.
 * 20) At what frequencies can the air in the tunnel resonate?
 * 21) Explain whether it would be good to make a rule against blowing your car horn when you are in the tunnel.


text:
Addiction

"Addiction is the physical and mental state of dependence on a substance or stimulus, to the point where withdrawal symptoms occur whenever the substance is not present in the body."

Addiction is defined as a chronic, relapsing brain disease that is characterized by compulsive behavior even in the presence of harmful consequences. The term addiction can be used in many ways, by some it is used to indicate only a neurological dependence on particular chemicals such as drugs. Addiction can also be described as dependence on various behaviors. It is only fairly recently that addiction has been studied scientifically. Addiction is a very powerful motivator that will often lead people to take actions despite harmful consequences.

Symptoms
There are a couple of symptoms following addiction, such as the inability to limit the use of a substance or activity beyond need. The addicted user is forced to increase either the dosage of the substance or time spent engaging in the addictive activity, indicating that more is needed to provide the desired effect (known as tolerance). Failing to fulfill the desire often produces symptoms of withdrawal, such as irritability, anxiety, shakes, nausea. The symptoms can move past the physical and into the psychological. While addiction in itself is partly a psychological disease, continued use can further promote feelings of shame, guilt, anxiety or depression, just to name a few. Symptoms can vary depending on the substance or activity that is used.

Disease model
Addiction is a disease. Progressive and incurable. Diagnosis is difficult and treatment limited.

title: Addiction


text: Category:Child psychology

title: Category:Child psychology