Chapter 8: Energy. P = W t. KE = 1 2 mv2. PE = mgh. Text: Chapter 8 (skip sections 8.7 to 8.9) Think and Explain: 1-4 Think and Solve: 1-3

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1 Text: Chapter 8 (skip sections 8.7 to 8.9) Think and Explain: 1-4 Think and Solve: 1-3 Chapter 8: Energy NAME: Vocabulary: Work, energy, Joule, Watt, kinetic energy, potential energy, mechanical energy, power, Conservation of Energy Equations: W = Fd P = W t KE = 1 2 mv2 PE = mgh Key Objectives: Concepts Relate the direction of force and distance to the work done on an object. Recognize when work is done against a force. Define power and state the units of power. Distinguish between mechanical energy and other forms of energy. Distinguish between potential energy and kinetic energy. Understand the concept of Conservation of Energy. Problem Solving Calculate the work done by a force acting over a distance. Calculate power in watts. Convert watts to kilowatts. Calculate the kinetic energy, potential energy, and total energy. Apply principle of energy conservation to problem solving. Make and interpret graphs of KE, PE and Total Energy vs time

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3 Work NAME: Normally, we would do a lab of some form to introduce a new idea or concept. While we will do a lab very soon, I want to introduce a new term to you that has a very specific definition: work. Tomorrow, we will get into why we care about work and what it does, but for today, let's just get used to doing some calculations based on the following initial definition of work: m F d The work W done by a force F that acts on an object for a distance d (as shown above) is W = Fd cosθ A. What are the units of work? B. Is work a vector or a scalar? C. Why is there a cosine in the equation? D. If the force F was parallel to the displacement (d), what would be the work done by F? E. If the force F was perpendicular to the displacement (d), what would be the work done by F? F. Can work be a negative number? Calculations m F d The diagram above shows a block being pulled across a floor or table by a horizontal force F. 1. If the force was a constant 20 N, how much work was done by the force pulling the object 5 m? 2. If the force was a constant 20 N, how much work was done by the force pulling the object 15 m? 3. How far would a force of 15 N have to pull the object to do 100 J of work? 4. If the distance pulled was 8 meters and the total work done was 90 J, what was the force? side 1

4 Work NAME: 5. If there was a friction force of 5 N, and the object was still pulled to the right 7 meters, how much work did friction do? 6. If friction did 75 J of work, and the object was pulled 8 meters, what was the force of friction? 7. Can friction ever do positive work? Explain. 8. A 35 N force is pulling a box to the right. There is also a frictional force of 15 N acting on the box. The box is pulled a total of 5 meters. a. How much work did the 35 N force do? b. How much work did friction do? c. How much total work was done on the box? 9. A 50 N force is pulling a box to the right a distance of 12 meters. Friction does 200 J of work on the box. a. How much work did the 50 N force do? b. What was the force of friction? c. How much total work was done on the box? Now imagine a force is pulling up at an angle, as shown to the right. The object moves horizontally. 10. How much work does a constant force of 25 N at an angle of 30º do when the object moves 5 m? m d F 11. How much work does a constant force of 25 N at an angle of 60º do when the object moves 5 m? 12. If the force was 75 N and the angle was 40º, how far was the box pulled if the work done by the force was 200 J? 13. Here's a tricky one! How much work did gravity do on the box in any of those problems? Answers: 1) 100 J 2) 300 J 3) 6.7 m 4) N 5) 35 J 6) 9.4 N 7) No! b/c always opposite the motion 8.a) 175 J b) 75 J c) 100 J 9.a) 600 J b) 16.7 N c) 400 J 10) J 11) 62.5 J 12) 3.48 m 13) 0 J! Force of gravity perpendicular to motion in all these problems. side 2

5 Lab 8-1: Making the Grade NAME: Purpose: To investigate the force, the distance, and the work involved in moving an object up an incline as the angle is changed yet the height to which it is lifted remains constant. Procedure: l. Place a clamp on a ring stand. Clamp the track in place at an angle of 15º, as shown in the figure below. Pull the cart up the inclined plane at a constant speed with a spring scale or force probe kept parallel to the plane, to measure the force. You need not pull it all the way up the ramp. Measure the distance from the bottom of the incline to the ring stand clamp. Record the force and distance in the data table. Also note the height and the weight of the cart. distance 30 cm Lab Table 2. Vary the angle while keeping the height the same by sliding the board up or down inside the clamp to make angles of 30º, 45º, and 60º. For each of the different angles, pull the cart parallel to the board. Record force and distance for each trial in the data table for Part Flip the cart over (so the wheels are up in the air), and repeat step 2 above. Record the data in Part 2. Data: Height for all trials 0.3 m Weight of cart N Part 1: Frictionless Angle of track Force (N) Distance (m) Work done (J) Part 2: Friction Angle of track Force (N) Distance (m) Work done (J) Calculations: l. For each trial, calculate the work done in pulling the cart up the hill. side 1

6 Lab 8-1: Making the Grade NAME: Questions: l. Why should the force probe be kept parallel to the board as the carts are pulled up the hill? 2. Show all the forces acting on the cart as it is moving up the hill at constant speed. Make all force vectors of appropriate length. 3. Is there a net force on the cart? Explain. 4. If you do work on an object, and that object does not change its speed, the work you did was done against some other force or forces. What force(s) did you do work against in this lab? Be specific and use your diagram from question 2 to help you. 5. In this lab, you dragged the cart along the ramp to the same final height. Suppose you lifted the wagon straight up to that same final height, and did not use the ramp. a. How much work would you do? b. Would you be doing any work against friction? Explain. W = J 6. What pattern or relationship do you find regarding the work done to get the cart to the top of the ramp at the 4 angles when there was little to no friction? Part II: 8. This time, was the work done the same each trial? 9. In which trial was the most work done? 10. What forces were you fighting in pulling the wooden block up the ramp? 11. If pulling something up a ramp actually requires more work, why would people use a ramp at all? What is the advantage? side 2

7 Quick Concepts A. In words, what is kinetic energy? Kinetic Energy NAME: B. What is the equation (and therefore the definition) of kinetic energy? C. What are the units used for kinetic energy? D. Is kinetic energy a vector or a scalar? Why? E. Can kinetic energy ever be negative? Why? Calculations 1. How much kinetic energy does a 65 kg person running at 2 m/s have? 2. How fast is a 1500 kg car moving if it has a kinetic energy of 200,000 J? 3. What is the mass of something moving at 12 m/s that has a kinetic energy of 1000 J? 4. What is the kinetic energy of a kg bee flying at 5 m/s? 5. A 1200 kg car is driving down the road with a speed of 5 m/s. a. What is the kinetic energy of the car? b. If the car gains 50,000 J of kinetic energy, how much kinetic energy would it have? c. And so how fast would it then be going? 6. A 3 kg box is sliding along the floor. It has an intial speed of 8 m/s. a. How much kinetic energy does it have? b. If it loses 60 J of kinetic energy, how fast will it be going? 7. If you gain kinetic energy, what has to happen to you? 8. If you lose kinetic energy, what has to happen to you? side 1

8 Kinetic Energy NAME: 9. Both momentum and kinetic energy depend on mass and velocity. a. Is it possible to have a constant kinetic energy, but a changing momentum? Explain. b. How about a constant momentum and a changing kinetic energy? Explain. 10. a. Which has more kinetic energy: a mass of 1 kg moving at 2 m/s or a mass of 2 kg moving at 1 m/s? b. Which has more momentum: a 1 kg object moving at 2 m/s or a 2 kg object moving at 1 m/s? 11. Imagine there are two objects traveling in opposite directions. A mass of 5 kg moving at 4 m/s to the left and a mass of 5 kg moving at 4 m/s to the right. a. What is the total kinetic energy of the two objects? b. What is the total momentum of the two objects? 12. Imagine you are driving down the road with a certain speed. a. If you double your speed, how much does your kinetic energy change? how about momentum? b. If you triple your speed, how much does your kinetic energy change? how about momentum? c. If you cut your speed in half, what happens to your kinetic energy? how about momentum? Answers: 1) 130 J 2) 16.3 m/s 3) 13.9 kg 4) J 5. a) 15,000 J b) 65,000 J c) 10.4 m/s 6. a) 96 J b) 4.9 m/s 7) speed up 8) slow down 9. a) Yes. Changing direction at constant speed. b) No. Constant momentum implies constant speed. 10. a) the 1 kg mass (2 J vs. 1 J) b) they are the same. both 2 kgm/s 11. a) 80 J b) 0 kgm/s 12. a) 4x K & 2x p b) 9x K & 3x p c) 1/4 K & 1/2 p side 2

9 Work & Kinetic Energy Quick Concepts A. What are the definitions of work and kinetic energy? NAME: B. How are work and kinetic energy related? C. If a force does negative work to something, what is the force trying to do? Calculations 1. A 100 Newton wind is blowing a 75 kg ice-boarder across a frozen frictionless pond for a distance of 50 meters. The ice-boarder started at rest. a. How much work did the wind do on the ice-boarder? b. What was the kinetic energy of the ice-boarder at the end of the 50 meters? c. How fast was the ice-boarder going at the end of the 50 meters? 2. A 1750 kg car is driving down the road with a speed of 15 m/s. The car speeds up through a force of 3500 N over a distance of 75 meters. a. What is the initial kinetic energy of the car? b. How much work did the force do on the car? c. What is the final kinetic energy of the car? d. What is the final velocity of the car? 3. Betty pushes her physics book (m=2 kg) with a speed of 4 m/s. She lets go, and the book slides to stop in 0.75 meters. a. What was the initial kinetic energy of the book? b. What was the final kinetic energy of the book? c. How much work did friction do? d. What was the force of friction on the book? 4. A 60 kg skier has a kinetic energy of 6750 J at the bottom of a hill, and skids to a stop in a distance of 35 meters. a. What was the velocity of the skier just before the skid? side 1

10 Work & Kinetic Energy NAME: b. What was the average force of friction on the skier while skidding? (Hint: how much work did friction do?) 5. You are pulling your 25 kg cousin in a toy wagon with a force of 150 N directed up at an angle of 40º and at a constant velocity. You pull for a distance of 250 meters. a. How much work did you do on your cousin? b. How much work did friction do on your cousin? c. Why did your cousin gain no kinetic energy? 6. Al is pulling Charlene (m=70 kg) with a force of 25 N for a distance of 20 meters. At the end of the 20 meters, Charlene has a speed of 3 m/s. Charlene's initial speed was 0 m/s. a. How much work did Al do on Charlene? b. What is Charlene's final kinetic energy? c. How much work did friction do? (Hint: Why are your answers to a and b different?) d. What was the average force of friction? 7. You are dragging a 25 kg sled across the snow with a force of 50 N at an angle of 30º above the horizontal. The sled starts at rest, and you drag it for 7 meters. a. How much work did you do on the sled? b. If the snow were frictionless, how fast would the sled be going at the end? c. If there was a friction force of 23 N, how much work would friction have done? d. So what would be the final speed if there was 23 N of friction? Answers: 1. a) 5000 J b) 5000 J c) 11.6 m/s 2. a) 197,000 J b) 263,000 J c) 460,000 J d) 22.9 m/s 3. a) 16 J b) 0 J c) -16 J d) N 4. a) 15 m/s b) -193 N 5. a) 28,700 J b) -28,700 J c) friction 6. a) 500 J b) 315 J c) -185 J d) -9.3 N 7. a) 303 J b) 4.92 m/s c) -161 J d) 3.37 m/s side 2

11 Kinetic and Potential Energy Practice NAME: 1. A 20 kg rock is lifted 5 m. a. What work was done against gravity? b. What is its gravitational potential energy? 2. A flower pot weighing 10 N is lifted and given 20 J of gravitational potential energy. How high was it lifted? 3. A 4000 kg roller coaster car is pulled to the top of the first hill, which is 30 m above the starting position. a. What is the gravitational potential energy of the car at the top of the hill? b. How much work was done on the car to get it to the top of the hill? c. What happens to this stored PE as the car travels down the hill? 4. A 10 kg object is moving along at a constant speed of 5 m/s. What is its kinetic energy? 5. If the speed of the object in question 4 doubles, by how much does the KE change? 6. A 5 kg ball is dropped out a window and hits the ground with 500 J of KE. With what speed does the ball hit the ground? 7. If the 5 kg ball hits the ground with 250 J of KE, what is the speed of the ball as it hits the ground? 8. A 0.5 kg lab cart is released on an inclined track. The cart is released from a height of 0.3 m and has a speed of 2.45 m/s at the bottom of the track. a. What is the PE of the cart at the top of the track? b. What is the KE of the cart at the top of the track? c. What is the KE of the car at the bottom of the track? d. Why are your answers to a and c the same? 9. A 1.5 kg cart is placed on a 0.35m high inclined track. a. What is the PE of the cart at the top of the track? side 1

12 Kinetic and Potential Energy Practice NAME: b. What happens to the PE as the cart rolls down the track? c. What is the KE of the cart at the bottom of the track? d. What is the speed of the cart at the bottom of the track? e. If you replaced the cart with a wooden block, would you expect the PE at the top to equal the KE at the bottom? Explain. 10. After graduation, an enthusiastic A-B graduate tosses her 150 g cap into the air with a speed of 6 m/s. a. What is the KE of the cap when it is released? b. What happens to the KE as the cap travels up? c. How high does the cap go? 11. A happy physics student decides to go sledding. He carries his sled (total mass 60 kg) up the hill and does 3300 J of work against gravity. a. How high is the hill? b. Assuming the snow is frictionless, how fast will the student and sled be moving at the bottom of the hill? c. Taking friction into account, would you expect the speed of the student to be more, less or the same as in part c? Explain in terms of energy. 12. Three physics teachers decided to slide down an icy hill. The first teacher has a mass of 60 kg, the second teacher has a mass of 68 kg and the third teacher has a mass of 80 kg. If the hill is 4 m high, which teacher has the greatest speed at the bottom of the hill? Answers: 1. a) 1000 J b) 1000 J 2) 2 m 3. a) 1,200,000 J b) 1,200,000 J c) turns into KE (& sound & heat) 4) 125 J 5) quadruples! (500 J) 6) 14.1 m/s 7) 10 m/s 8. a) 1.5 J b) 0 J c) 1.5 J d) conservation of energy 9. a) 5.25 J b) KE c) 5.25 J d) 2.6 m/s e) PE>KE, Friction 10. a) 2.7 J b) PE c) 1.8 m 11. a) 5.5 m b) 10.4 m/s c) less 12) they all will have the same speed at the bottom side 2

13 Lab 8-2: Energy of a Tossed Ball NAME: Purpose: 1. To examine graphs of kinetic and potential energy for a toy ball that is tossed up in the air. 2. To see how the total energy of a ball changes as it goes up and down after tossing it in the air. Preliminary Questions: In the following questions, imagine tossing a ball over a motion detector and catching it when it comes back down. Only consider the motion of the ball while it is in the air. 1. What form or forms of energy does the ball have while momentarily at rest at the top of the path? 2. What form or forms of energy does the ball have while in motion near the bottom of the path? 3. What does a height of zero mean to the motion detector? 4. Sketch graphs of position vs time and velocity vs. time for the ball while it is in the air. Identify the portions that correspond to the release of the ball, at its maximum height, and when you catch it again. H V 5. Sketch graphs of potential energy vs. time and kinetic energy vs time for the ball while it is in the air. PE KE 6. If there are no frictional forces acting on the ball, how is the change in the ball s potential energy related to the change in kinetic energy? Procedure: l. Start Logger Pro by opening up the file that your teacher told you to open up. Look on the board if you didn t pay attention to your teacher. 2. Enter the mass of the ball in the lower right corner of the screen. 3. Place the motion detector on a stool pointing up, and toss the ball up in the air a couple times. With a little luck, one of the tosses will show a nice set of graphs. Zoom in on a nice toss (or just ignore the messy ones.) 4. Click on the Examine tool and move the mouse across the distance or velocity graphs of the motion of the ball to answer these questions: a. Identify the portion of each graph where the ball had just left your hands and was in free fall. Determine the height and velocity of the ball at this time. Enter your values in the data table. side 1

14 Lab 8-2: Energy of a Tossed Ball NAME: b. Identify the point on each graph where the ball was at the top of its path. Determine the time, height, and velocity of the ball at this point. Enter your values in the data table. c. Find a time where the ball was moving downward, but a short time before it was caught. Measure and record the height and velocity of the ball at that time. d. For each of the three points in the data table, calculate the Potential Energy (PE), Kinetic Energy (KE), and Total Energy (TE). Use the position of the Motion Detector as the zero of your gravitational potential energy. Show your calculations below, and record the answers in the data table. Data: Position Height Velocity PE KE TE (m) (m/s) (J) (J) (J) After release On the way up Top of path Before catch Conclusions: 1. How well do the calculations above show conservation of energy? Explain. 2. Click on the top graph s vertical axis label and change the display to Kinetic Energy, KE. Inspect your kinetic energy vs. time graph for the toss of the ball. Sketch the shape of the graph while the ball was in the air and explain what happens to the kinetic energy of the ball while it is in the air. KE t 3. Click on the bottom graph s vertical axis and change the display to the Potential Energy, PE. Inspect your potential energy vs. time graph for the toss of the ball. Sketch the shape of the graph while the ball was in the air and explain what happens to the kinetic energy of the ball while it is in the air. PE t side 2

15 Lab 8-2: Energy of a Tossed Ball NAME: 4. Compare your energy graphs predictions (from the Preliminary Questions) to the real data for the ball toss. 5. Click on the vertical axis of the KE graph and choose More then check Potential energy and click ok. You should now have both the KE and PE graphs on the same graph (rescale if needed). Notice that when KE=0 PE is at a maximum. Why is PE not equal to zero when KE is at a maximum? 6. Logger Pro will also calculate Total Energy, the sum of KE and PE. Click on the top graph s vertical axis label, choose More and add the Total Energy to the graph. Sketch the shape of the graph of Total Energy vs time and explain what happens to it while the ball was in the air. TE t 7. What do you conclude from this graph about the total energy of the ball as it moved up and down in free fall? Was energy conserved? 8. Would the shapes of the graphs you made change if you had entered the wrong mass for the ball? Explain. Follow-Up Questions: 1. A ball is tossed up in the air with 50 J of kinetic energy. Its initial height is 0 meters. a. What is its potential energy? How about its total energy? b. As it goes up in the air, what happens to its kinetic energy? c. As it goes up in the air, what happens to its total mechanical energy? d. At its maximum height, what is its kinetic energy? potential energy? total energy? e. At some point, the balls kinetic energy is 30 J. What is its potential energy? total energy? f. At some point, the balls potential energy is 40 J. What is its kinetic energy? total energy? g. Where is it when: i) its potential energy equals its kinetic energy? side 3

16 Lab 8-2: Energy of a Tossed Ball NAME: ii) its total energy equals its kinetic energy? iii) its total energy equals its potential energy? 2. The following graphs all came from this lab. Label them correctly (include units.) 3. Some other students did the same lab with a 0.25 kg ball. They recorded the initial height and velocity of the ball as shown in the table. Fill in the rest of the table. Here are some hints: What is the kinetic energy of the ball at its maximum height? What number stays constant even though the ball is going up and down and changing speeds? (mass = 0.25 kg) Height (m) Velocity (m/s) PE (J) KE (J) TE (J) Initial Data Top of Path Random Position Explain how the following statement applies to this lab: "Energy can not be created or destroyed, but it can change forms." side 4

17 Conservation of Energy (no friction) NAME: 1. A highdiver (m = 75 kg) is standing atop a 60 meter tall tower and then jumps to a pool below. a. How much potential energy does the diver have at the top of the tower? b. How much potential energy does the diver have when they hit the water? c. How much kinetic energy does the diver have at the top of the tower? d. How much kinetic energy does the diver have when they hit the water? e. How much total energy did the diver have as they fell? f. When the diver was halfway down, how much potential and kinetic energy did the diver have? g. How fast was the diver going just as they hit the water? 2. Charlene has a mass of 70 kg and is jumping on a trampoline. The trampoline gives her an initial velocity of 12 m/s straight up. a. How much kinetic energy does she have as she leaves the trampoline? b. How much kinetic energy does she have at her highest point? c. How much potential energy does she have as she leaves the trampoline? d. How much potential energy does she have at her highest point? e. How high up does she go? f. When she is one meter above the trampoline, what is her total energy? 3. You toss your 7 kg backpack straight up in the air, giving it a kinetic energy of 120 J. a. How fast did you throw it? b. How high does it go? 4. A 72 kg skier is at the top a frictionless hill with a vertical drop of 95 meters. a. How much potential energy does the skier have at the top of the hill? b. How fast is the skier going at the bottom of the hill? c. How much work did gravity do on the skier? side 1

18 Conservation of Energy (no friction) NAME: 5. A 1500 kg car is stopped on a hill when the brakes fail (i.e. no friction) and it rolls down the hill. The car rolls until it has speed of 3 m/s. a. How much kinetic energy does the car have a the bottom? b. What was the vertical drop of the car on the hill? c. How much work would it take to stop the car? d. If the car were to crash into a tree at the bottom of the hill, and the hood is pushed in.25 meters, what was the average force of the tree on the car? 6. A frustrated painter throws his brush (m = 0.04 kg) straight up in the air with an initial velocity of 23 m/s. How high does the brush go? 7. A 32 kg child is having fun at the playground on a Super Slide. It is 4.5 meters high and absolutely frictionless. How fast is the child going at the bottom of the slide? 8. A 1300 kg roller coaster car is 45 meters high in the air. It rolls down a frictionless hill, and falls a vertical distance of 25 meters to the bottom of the first hill. How fast is the roller coaster car traveling at the bottom of the first hill? 9. The drawing below represents a frictionless hill, with lines of equal height shown. A ball is given an initial kinetic energy at point A, and then the position of the ball is shown at several positions later. A B C D E F G H I J K L M For each of the questions below, rank the position from greatest to least a. Where is the ball going the fastest? b. Where does the ball have the most potential energy? c. Where does the ball have the most total energy? Answers: 1. a) 45,000 J b) 0 J c) 0 J d) 45,000 J e) 45,000 J f) 22,500 & 22,500 J g) 34.6 m/s 2. a) 5040 J b) 0 J c) 0 J d) 5040 J e) 7.2 m f) 5040 J 3. a) 5.86 m/s b) 1.71 m 4. a) 68,400 J b) 43.6 m/s c) 68,400 J 5. a) 6750 J b) 0.45 m c) 6750 J d) 27,000 N 6) 26.5 m 7) 9.49 m/s 8) 22.4 m/s 9. a) H b) A c) all the same! side 2

19 Lab 8-3: Conservation of Energy NAME: Purpose: To examine the changes in potential, kinetic and total energy for a cart that is being pulled by a hanging mass. Materials: 1 cart 1 pulley 1 track string 1 50 gram hanger Procedure: 1. Set up the apparatus as diagrammed below. 2. Start Logger Pro and open up the file "02 Cart," as you usually do. empty cart (first trial) > 20 cm lab table empty hanger 3. Hold the cart so that it is not moving and click on the blue "zero" button, which is next to the green "collect" button. Say ok to to zero the motion detector. You will then hear a couple clicks from the motion detector - this will be Logger Pro making the position of the motion detector equal to zero. 4. Click on the collect button, and then release the cart. 5. Using the "examine" tool, determine the speed and position of the cart before it hits the ground and record those numbers in the data table. 6. Add 50 grams to the hanger and repeat above. You will have to zero the motion detector again. 7. Remove the extra 50 grams from the hanger, but put a black bar in the cart, and repeat above. Data: Trial 1 Trial 2 Trial 3 Hanger Mass (kg) 0.05 kg 0.10 kg 0.05 kg Mass of Cart (kg) 0.50 kg 0.50 kg 1.00 kg Total Mass (kg) Initial Speed (m/s) 0 m/s 0 m/s 0 m/s Distance Fallen (m) Final Speed (m/s) side 1

20 Lab 8-3: Conservation of Energy NAME: Calculations: For each of the questions below, show your work in the space provided and then write the answers in the table below. Make sure to include the equation you are using. l Determine the total kinetic energy of the mass and the hanger before you let them go. K i cart: + K i hanger: = Total K i : 2. Calculate the PE "lost" by the falling mass in each trial. 3. Calculate the total kinetic energy of the mass and the hanger after you let them go. K f cart: + K f hanger: = Total K f : KE initial of cart and hanger (J) PE lost by hanger (J) KE final of cart and hanger (J) Summary of Calculations Trial 1 Trial 2 Trial 3 Conclusion: 1. Was energy conserved? Explain. 2. What would have happened if you used the friction blocks instead of the carts? Explain. Both the cart and the hanger moved the same distance and they always the same speeds. 3. Which object lost potential energy? Explain. 4. Which object gained kinetic energy? Explain. side 2

21 Lab 8-3 Problems NAME: frictionless 1. A 500 gram cart is attached to a 100 gram mass as shown in the picture above. The system is held at rest, and then released, and then the little mass falls 25 cm, pulling the cart along with it. a. How much potential energy does the 100 gram mass lose while falling? b. How much potential energy does the 500 gram cart lose while moving to the right? c. What happens to the potential energy that is lost? d. How fast are the cart and mass going at the end of the 25 cm? 2. A 500 gram cart is on a horizontal frictionless table and is attached through a pulley to a 150 gram mass. Everything is held at rest, and then released. After the little mass falls 0.35 meters, how fast are the cart and mass moving? 3. A 250 gram mass is hanging from a string that is connected via a pulley to a 400 gram cart which is itself on a horizontal frictionless table. The system is initially at rest. After the 250 gram mass falls a distance h, the cart and mass have a speed of 0.75 m/s. a. How much kinetic energy did the little mass gain while falling? b. How much kinetic energy did the cart gain while moving to the right? c. Where did all this kinetic energy come from? d. What was the distance h? 4. If the cart was 1.5 kg and the little mass was 0.25 kg and the cart moved to the right 0.45 m after being released, how fast was the cart going at the end of the 0.45 m? 5. If the little mass was 0.3 kg and it had a speed of 1.2 m/s after falling a distance of 0.45 m, what was the mass of the cart? Answers: 1. a) 0.25 J b) 0 J c) KE of both masses d) 0.91 m/s 2) 1.27 m/s 3. a) 0.07 J b) 0.11 J c) PE "lost" by 0.25 kg mass d) m 4) 1.13 m/s 5) 1.58 kg

22 Lab 8-4: Power NAME: Purpose: To determine your horsepower as you do work against gravity running up stairs. Procedure: 1. Calculate your mass in kg from your weight in pounds. Show your work in the table, and record your answer in the table below. Use the conversion factor 1 kg = 2.2 lbs. 2. In the stairwell, measure the height from the first floor to the second floor, and record this in the answer column of row Time how long it takes you to go from the first floor to the second floor and record this in the answer column of row Complete each row of the data table below showing your work in the middle column and the answer in the answer column. Data: Show Work Here Answer 1. Your mass (kg) 2. Height through which you lifted your mass against gravity (m) data from class 3. Time to do this work (s) data from class Force you used to lift your mass (your weight) (N) Work done by you to get to the top of the stairs (J) 6. Power you generated (W) 4.13 m 7. Horsepower (750 W = l hp) Questions: 1. What was your horsepower? How long do you think you could do that amount of horsepower (a couple minutes, a few hours, all day, etc.) 2. What was the biggest horsepower generated in the class? 3. What is meant by the term work? 4. What is meant by the term power? 5. Do the calculations depend on you hitting every step or could you do two steps at once? 6. Against what did you do your work?

23 A. What is meant by the term "work?" Power NAME: B. What is power? C. What are the units of power? Calculations 1. What is the power of a person that can do 5000 J of work in 4 seconds? 2. A force does 500 J of work in 1 minute. What is the power of the force? 3. How much energy is used by a 75 W light bulb in 2 minutes? 4. How much energy does a 4500 W generator produce if it is running for 6 hours? 5. How long would it take a 40 W engine to do 5000 J of work? 6. How long would take something producing 250 W to do 1,000 J of work? How about 10,000 J? 7. How much power does it take to lift 20 kg to a height of 15 meters in only 5 seconds? 8. How long would it take a 5,000 W crane to lift 150 kg to a height of 30 meters? 9. Every year, there is a race at the Empire State Building, from the ground floor to the 86th floor observation deck. The participants climb 1576 stairs for a total height of 320 meters. a. The record for this event is a time of 9 minutes and 33 seconds. If that person had a mass of 70 kg, what was the power needed? b. Using your power output from the Power Lab, how long would it take you to complete this task? Do you think that is a realistic estimate of how long it take you to do this? 10. Which is more powerful: doing 1000 J of work in 50 seconds or doing 500 J of work in 25 seconds? Answers: 1) 1250 W 2) 8.3 W 3) 9000 J 4) 97,200,000 J 5) 125 s 6) 4 s; 40 s 7) 600 W 8) 9 s 9. a) 391 W b) ) same, both 20 W side 1

24 Conservation of Energy Concepts A. What are the two key ideas in the Law of Conservation of Energy? NAME: B. Give an example of each of the following types of energy: kinetic energy gravitational potential energy chemical potential energy elastic potential energy msgnetic potential energy electric potential energy thermal energy C. What type(s) of energy are in each of the following: an explosion a moving ball a battery gasoline an orange a lightbulb (on) Applications For each of the following situations, explain the energy transformations that take place. 1. What does a generator do? 2. You plug in your phone all night. 3. You use your phone all day. 4. You use a flashlight. 5. You use the brakes the stop your normal car. 6. You slow down in your hybrid car. 7. What does a car engine do? 8. What does photosynthesis do? 9. You rub your hands together. 10. Some dynamite explodes. side 1

25 Work and Power Practice NAME: 1. On his way off to college, Drew drags his suitcase 15.0 m from the door of his house to the car at a constant speed with a horizontal force of 95 N. a. How much work does Drew do to overcome friction? b. Against what force does Drew do work? 2. Katie, a 30 kg child, climbs a tree to rescue her cat that is afraid to jump 8.0 m to the ground. a. Against what force does Katie do work? b. How much work does Katie do? 3. Marina does 3.2 J of work to lower the window shade in her bedroom a distance of 0.80 m. How much force must Marina exert? 4. At Six Flags, a ride called the Cyclone is a giant wooden roller coaster that ascends a 34.1 m hill and drops 21.9 m before ascending the next hill. The train of cars has a mass of 4700 kg. a. How much work is required to get the train of cars from the ground to the top of the first hill? b. What power is generated to bring the train of cars up in 30 s? 5. A box weighing 2000 N is dragged up a 3 m long incline with a force of 1500 N. The top of the incline is 1.5 m above the ground. a. When dragging the box along the incline, how much work is done? b. What is this work done against? c. If you lifted the box to a height of 1.5m, how much work would you do? Side 1

26 Work and Power Practice NAME: d. What force do you do work against when lifting the box? e. Why use a ramp if it requires more work? 6. Jack (30 kg) and Jill (20 kg) went up the hill to see who could generate the most power when doing work against gravity. They ran up a hill with a vertical height of 12 m. Jack reached the top in 6.8 seconds and Jill reached the top in 5.0 seconds. a. Who did more work? b. Who was more powerful? 7. Gary holds a 4 N book stationary 2 m above the ground. How much work does Gary do on the book? Answers: 1. a) 1425 J b) friction 2.a) gravity b) 2400 J 3) 4 N 4. a) 1,603,000 J b) 53,400 W 5. a) 4500 J b) friction & gravity c) 3000 J d) only gravity e) still less force 6. a) Jack = 3600 J & Jill = 2400 J b) Jack = 530 W & Jill = 480 W 7) none. (its not moving, so no displacement, so no work.) Side 2