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WORK & POWER

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ENERGY

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Name _________ Work and Power Date _________

1. Brutus, a champion weightlifter, raises 260 kg of weights a distance of 2.25 m.

[pic]

a) How much work is done by Brutus?

b) How much work is done by Brutus holding the weights above his head?

c) How much work is done by Brutus lowering them back to the ground?

d) Does Brutus do work if he lets go of the weights and they fall to the ground?

e) If Brutus completes the lift in 1.9 s, how much power is developed?

2. A horizontal force of 805 N is needed to drag a crate across a horizontal floor with a constant speed. You drag the crate using a rope held at an angle of 32(.

a) What force do you exert on the rope?

b) How much work do you do on the crate when moving 22 m?

c) If you complete the job in 8.0 s, what power is developed?

3. An airplane passenger carries a 223 N suitcase up the stairs, a displacement of 5.3 m horizontally and 5.6 m vertically.

a) How much work does the passenger do?

b) The same passenger carries the same suitcase back down the same stairs. How much work does the passenger do now?

Reference: Figure B

A 1.0 kg box, initially at rest and a height of 30.0 m, begins sliding down a frictionless surface. When it reaches the bottom it starts sliding across the horizontal surface, then has a totally inelastic collision with a 2.0 kg box. They stick together and begin to slide off together. After leaving this surface, the system is projected horizontally, from a vertical height of 5.0m.

A) Calculate the speed of the 1.0 kg box at the bottom of the hill (before striking M2).

B) Calculate the speed of the two boxes after they collide.

C) Calculate the speed that the system has when it leaves the surface without friction and becomes a projectile.

D) Calculate the horizontal range of this projectile.

Figure B:

WORK, POWER, KINETIC ENERGY & POTENTIAL ENERGY

|Description |+ or - Work? |Change PE or KE or Both? |

|Megan drops the ball and hits an awesome forehand. The racket is moving horizontally as the |  |  |

|strings apply a horizontal force while in contact with the ball. | | |

|[pic] | | |

|A baseball player hits the ball into the outfield bleachers. During the contact time between |  |  |

|ball and bat, the bat is moving at a 10 degree angle to the horizontal. | | |

|[pic] | | |

|Rusty Nales pounds a nail into a block of wood. The hammer head is moving horizontally when it |  |  |

|applies force to the nail. | | |

|[pic] | | |

|The frictional force between highway and tires pushes backwards on the tires of a skidding car.|  |  |

|[pic] | | |

|A diver experiences a horizontal reaction force exerted by the blocks upon her feet at start of|  |  |

|the race. | | |

|[pic] | | |

|A weightlifter applies a force to lift a barbell above his head at constant speed. |  | |

|[pic] | | |

|Description of Motion |KE to PE or PE to KE? |

| |Explain. |

|1. |A ball falls from a height of 2 meters in the absence|

|  |of air resistance. |

| |[pic] |

|2. |A skier glides from location A to location B across |

| |the friction free ice. |

| |[pic] |

|3. |A baseball is traveling upward towards a man in the |

| |bleachers. |

| |[pic] |

|4. |A bungee chord begins to exert an upward force upon a|

| |falling bungee jumper. |

| |[pic] |

|5. |The spring of a dart gun exerts a force on a dart as |

| |it is launched from an initial rest position. |

| |[pic] |

Work, Energy, and Power Study Guide

Name:____________ Date:_________

1. Work is done only if the object pushed is ___________ .

2. Potential energy depends upon what three variables?

a. ________________

b. ________________

c. ________________

3. What variables do momentum and kinetic energy have in common?

a. ________________

b. ________________

4. Energy is the ability of an object to make a ____________ in itself or the environment.

5. List several different types of energy.

a. ________________

b. ________________

c. ________________

d. ________________

6. ____________ is the process of changing the energy of the system.

7. Work is only done if the object is displaced by the__________, in the same direction as the _________! (same word for both blanks)

8. ___________ is the rate at which work is done.

9. Draw before and after pictures of a collision containing two motion carts of the same mass. The carts stick together after the collision.

10. Represent the above picture with an equation.

11. The above equation is referred to as the Law of ___________of _______________.

12. Power is measured in ___________.

13. Energy is measured in ___________.

14. Work done on a system results in ________ energy.

15. Stored energy is referred to as ________ energy.

16. The work-energy theorem states that ________ is equal to _________.

17. Sometimes we say that the energy was lost due to several different variables. Is the energy truly lost? ____ Where does it go? ____________________________________________________

18. When an object is dropped, it immediately begins to transfer ___________ energy to ___________ energy.

19. A skier starts from rest at the top of a 45-m hill, skies down at 30 degrees into a valley, and continues up a 40-m hill. Both hill heights are measured from the valley floor. Neglect friction.

a. How fast is the skier moving at the bottom of the first hill?

b. What is the skier’s speed at the top of the next hill?

c. Do your answers depend on the angle of the hill? _____ Why, Why not? ________________________________________

____________________________________________________________________________________________________

20. A 4200-N piano is slid up a 3.5-m plank at a constant speed. The plank makes an angle of 30 degrees with the horizontal.

a. What is the total height the piano is displaced?

b. Calculate the work done by the person sliding it up the incline.

c. If the worker does the job in 60 seconds, what power do they generate?

21. A 90-kg rock climber first climbs 45-m up to the top of a quarry, then descends 85-m from the top to the bottom of the quarry. If the initial height is the reference level, find the potential energy of the climber at the top and the bottom. Draw bar graphs for both situations.

Projectiles & Energy Conservation

Pre-Lab

|Experimental (Method 1) |Theoretical (Method 2) |

|Projectile Method |Conservation of Energy Method |

|1. Launch car |1. Determine total energy of the system using the total mass, |

|- measure dx, dy, and h as discussed in class. |gravitational acceleration, and initial height of the projectile.|

|2. Determine ‘t’ using projectile method (using dy = Vyi t + ½ |2. PE = mgh, where ‘h’ is the total height of the projectile |

|at2) |before the launch (htot = h + Δy as shown below). |

|3. Using ‘t’, solve for Vx… |3. Notice that the PE determined above is converted into the KE |

|Vx = dx / t |the projectile experiences throughout the “trip”. (PE = KE) |

|4. Solve for Vy… |4. THEORETICAL PE at the top is ideally equal to KE at the |

|Vyf2 = Vyi2 + 2ad |bottom! |

|5. Solve for Vtot, using vector analysis… Pythagorean Theorum | |

|6. Using Vtot, and the KE equation determine the EXPERIMENTAL KE.| |

|7. KE = the energy of the system | |

After solving for the energy of the system using both method 1 & 2, determine the “energy loss” of the system! (theoretical minus experimental).

Name _______________________ Period _______ Date ___________

CONSERVATION OF ENERGY LABORATORY

Purpose: The purpose of this lab is to apply the law of conservation of energy and the principle governing projectile motion to determine the amount of energy lost to friction as a matchbox car rolls down a ramp.

Background and Theory: There are several ways that the motion of objects can be analyzed. One way is by using kinematic equations and the idea of independence of horizontal and vertical components of the motion. Another way is by using the Law of Conservation of Mechanical Energy. In this laboratory, both methods will be used in determining the mechanical energy “lost” due to the dissipative force of friction. It is important to remember that the energy is not actually gone; rather it is converted into some other form.

When using the Law of Conservation of Mechanical Energy, conditions are assumed to be ideal, with no dissipative forces involved. Realistically, however, as a car rolls down a ramp, the force of friction does lead to a loss of mechanical energy. In calculating the mechanical energy at the bottom of the ramp, the value will be higher than it should be, since the force of friction has not been considered. By finding the actual velocity at the bottom of the ramp using projectile motion methods, a more accurate value of the energy can be obtained. The difference in the energy values of each method gives a good indication of how much energy was “lost” to friction.

Materials: matchbox car, ramp, meter stick, tape

Procedure:

1. Set up the apparatus as demonstrated.

2. Measure the height (h) to the top of the track in reference to the table top.

3. Measure the height of the table (Δdy).

4. Set your matchbox car at the top of the ramp, launch it, and note its approximate landing position on the floor.

5. Place a piece of carbon paper on top of a piece of notebook paper on the floor where the car landed.

6. Measure the horizontal distance (Δx) from the point of launch at the end of the ramp to the landing location of the car.

Data and Calculations:

Table 1: Raw Data

|Trial |dy (m) |h (m) | htot (m) |dx (m) |m (kg) |

|1 | | | | | |

|2 |“ |“ |“ | |“ |

|3 |“ |“ |“ | |“ |

Table 2: Calculated data

|Trial |Method 1 (projectile motion) |Method 2 (PE = mgh = KE) |

| |IN PRACTICE |IN THEORY |

| |Vx (m/s) |Vy (m/s) |Vtot (m/s) |KE (1) (J) |PE (J) |KE (J) |Energy Loss (J) |

|1 | | | | | |0 | |

|2 | |“ | | |“ |0 | |

|3 | |“ | | |“ |0 | |

|Ave | |“ | | | |0 | |

*Show one sample calculation for each variable of table 2 in lab notebook.

Analysis:

1. In which method of calculating kinetic energy should you reach a result that is closer to the “actual” kinetic energy of the car? Why?

2. In which method of calculating kinetic energy will the answer be true only if there was no friction or outside forces acting on the system?

3. In this lab, you calculated an energy loss. Where did this energy go? In what form was it lost?

4. Explain the main idea behind this lab. Specifically: Why are we able to subtract the kinetic energies from each method to find the energy lost to friction?

Energy of a Tossed Ball

When a juggler tosses a bean ball straight upward, the ball slows down until it reaches the top of its path and then speeds up on its way back down. In terms of energy, when the ball is released it has kinetic energy, KE. As it rises during its free-fall phase it slows down, loses kinetic energy, and gains gravitational potential energy, PE. As it starts down, still in free fall, the stored gravitational potential energy is converted back into kinetic energy as the object falls.

If there is no work done by frictional forces, the total energy will remain constant. In this experiment, we will see if this works out for the toss of a ball.

[pic]

In this experiment, we will study these energy changes using a Motion Detector.

objectives

1. MEASURE THE CHANGE IN THE KINETIC AND POTENTIAL ENERGIES AS A BALL MOVES IN FREE FALL.

2. See how the total energy of the ball changes during free fall.

Materials

|COMPUTER |volleyball, basketball, or other similar, fairly heavy ball |

|Vernier computer interface | |

|Logger Pro | |

|Vernier Motion Detector | |

Preliminary questions

FOR EACH QUESTION, CONSIDER THE FREE-FALL PORTION OF THE MOTION OF A BALL TOSSED STRAIGHT UPWARD, STARTING JUST AS THE BALL IS RELEASED TO JUST BEFORE IT IS CAUGHT. ASSUME THAT THERE IS VERY LITTLE AIR RESISTANCE.

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. Sketch a graph of velocity vs. time for the ball.

4. Sketch a graph of kinetic energy vs. time for the ball.

5. Sketch a graph of potential energy vs. time for the ball.

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

1. MEASURE AND RECORD THE MASS OF THE BALL YOU PLAN TO USE IN THIS EXPERIMENT.

2. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. Place the Motion Detector on the floor and protect it by placing a wire basket over it.

3. Open the file “16 Energy of a Tossed Ball” from the Physics with Vernier folder.

4. Hold the ball directly above and about 1.0 m from the Motion Detector. In this step, you will toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector. Have your partner click [pic] to begin data collection. Toss the ball straight up after you hear the Motion Detector begin to click. Use two hands. Be sure to pull your hands away from the ball after it starts moving so they are not picked up by the Motion Detector. Throw the ball so it reaches maximum height of about 1.5 m above the Motion Detector. Verify that the position vs. time graph corresponding to the free-fall motion is parabolic in shape, without spikes or flat regions, before you continue. This step may require some practice. If necessary, repeat the toss, until you get a good graph. When you have good data on the screen, proceed to the Analysis section.

Data Table

|MASS OF THE BALL |(KG) | |

|Position |Time |Height |Velocity |PE |KE |TE |

| |(s) |(m) |(m/s) |(J) |(J) |(J) |

|After release | | | | | | |

|Top of path | | | | | | |

|Before catch | | | | | | |

ANALYSIS

1. CLICK ON THE EXAMINE TOOL, [pic], AND MOVE THE MOUSE ACROSS THE POSITION 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 your data table.

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 your 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 your 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.

2. How well does this part of the experiment show conservation of energy? Explain.

3. Logger Pro can graph the ball’s kinetic energy according to KE = ½ mv2 if you supply the ball’s mass. To do this, choose Column Options[pic]Kinetic Energy from the Data menu. Click the Column Definition tab.You will see a dialog box containing an approximate formula for calculating the KE of the ball. Edit the formula to reflect the mass of the ball and click [pic].

4. Logger Pro can also calculate the ball’s potential energy according to PE = mgh. Here m is the mass of the ball, g the free-fall acceleration, and h is the vertical height of the ball measured from the position of the Motion Detector. As before, you will need to supply the mass of the ball. To do this, choose Column Options[pic]Potential Energy from the Data menu. Click the Column Definition tab. You will see a dialog box containing an approximate formula for calculating the PE of the ball. Edit the formula to reflect the mass of the ball and click [pic].

5. Go to the next page by clicking on the Next Page button, [pic].

6. Inspect your kinetic energy vs. time graph for the toss of the ball. Explain its shape.

7. Inspect your potential energy vs. time graph for the free-fall flight of the ball. Explain its shape.

8. Record the two energy graphs by printing or sketching.

9. Compare your energy graphs predictions (from the Preliminary Questions) to the real data for the ball toss.

10. Logger Pro will also calculate Total Energy, the sum of KE and PE, for plotting. Record the graph by printing or sketching.

11. What do you conclude from this graph about the total energy of the ball as it moved up and down in free fall? Does the total energy remain constant?

12. Should the total energy remain constant? Why?

13. If it does not, what sources of extra energy are there or where could the missing energy have gone?

THOUGHT EXPERIMENTS (DO NOT PERFORM, JUST PREDICT)

1. WHAT WOULD CHANGE IN THIS EXPERIMENT IF YOU USED A VERY LIGHT BALL, LIKE A BEACH BALL?

2. What would happen to your experimental results if you entered the wrong mass for the ball in this experiment?

3. Predict what would happen in a similar experiment using a bouncing ball. To do this, you would mount the Motion Detector high and pointed downward so it can follow the ball through several bounces.

STUDY GUIDE II

Part I - Mechanical Energy

|[pic] |[pic] |[pic] |[pic] |

1. Identical twins Pat and Chris are painting a house. Pat is standing on the scaffolding 5 meters above the ground. Chris is standing on the scaffolding 5 meters above Pat. Who has more potential energy? Explain.

2. Jared and Clay are climbing the stairs. Jared gets tired and stops halfway to the fourth floor. Clay makes it to the fourth floor without a problem. If Jared is twice as heavy as Clay, who has more potential energy? Explain.

3. A person weighing 630 N climbs up a ladder to a height of 5 meters. How much work does the person do? Determine the increase in the potential energy of the person from the ground to this height. Where does the energy come from to cause this increase in PE?

4. Calculate the kinetic energy of a 750 kg car moving at 13.9 m/s. What is the kinetic energy of the car if the speed is doubled? How much work must be done to double the speed?

5. A rifle can shoot a 4.2 g bullet at a speed of 965 m/s. Find the kinetic energy of the bullet. What work is done on the bullet if it starts from rest? If the work is done over a distance of 75 cm, determine the average force acting on the bullet.

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Part II – Problem Solving with Conservation of Energy

|[pic] |[pic] |[pic] |

1. A large chunk of ice with mass 15 kg falls from a roof 8 meters above the ground. Find the kinetic energy of the ice when it reaches the ground. What is the speed of the ice when it reaches the ground?

[pic]

2. A bike rider approaches a hill with a speed of 8.5 m/s. The total mass of the bike and the rider is 85 kg. Find the kinetic energy of the bike and rider. If the rider coasts up the hill, calculate the height at which the bike will come to a stop. (Assume there is no friction.) How would your answer vary if the mass of the bike and rider were doubled?

3. A 2 kg rocket is launched straight up into the air with a speed that allows it to reach a height of 100 meters, even though air resistance performs 800 J of work on the rocket. Determine the launch speed of the rocket. How high would the rocket travel if air resistance is ignored?

|4. Calculate the |[pic] |

|potential energy, | |

|kinetic energy, | |

|mechanical energy, | |

|velocity, and height of| |

|the skater at the | |

|various locations. | |

Part III – Problem Solving with Conservation of Energy

|[pic] |[pic] |[pic] |

|[pic] |[pic] |

1. A 20 kg rock is on the edge of a 100 meter cliff. Calculate the potential energy of the rock. If the rock falls off the cliff, what is its kinetic energy just before striking the ground? What speed does the rock have as it strikes the ground?

2. A physics book is dropped 4.5 meters. What speed does the book have just before it hits the ground?

3. From what height would a compact car have to be dropped to have the same kinetic energy that is has when being driven at 100 km/hr?

4. A 70 kg high jumper leaves the ground with a speed of 6 m/s. How high can he jump?

5. Just before striking the ground, a 900 kg Smart Bomb has 88.2 MJ of kinetic energy. If air resistance is ignored, determine the height from which the Smart Bomb was dropped. Determine the drop height if air resistance performs 8.82 MJ of work against the bomb as it falls towards its target.

6. A 74 kg student, starting from rest, slides down an 11.8 meter high water slide. On the way down, friction does 5600 J of work on him. How fast is he going at the bottom of the slide?

7. Block A with a mass of 12 kg moving at 2.4 m/s makes a perfectly elastic head-on collision with block B, mass 36 kg, at rest. Find the velocities of the two blocks after the collision. Assume all motion is in one dimension.

|8. Calculate the |[pic] |

|potential energy, | |

|kinetic energy, | |

|mechanical energy, | |

|velocity, and height| |

|of the ball at the | |

|various locations. | |

Part IV - Chapter Review

|[pic] |[pic] |[pic] |

|[pic] |[pic] |

1. Jamie lifts her toys into her tree house using a homemade elevator. The elevator has a mass of 2.5 kg and the tree house is 8 meters above the ground. How much work does Jamie do when lifting 5 kg of toys into the house? Determine the power used to lift the toys in 5 sec.

2. Mike pulls a sled across level snow with a force of 225 N using a rope that is angled at 35(. Determine the work done if he pulls the sled 65.3 meters.

3. A 2 kg textbook is lifted from the floor to a shelf 2.1 meters above the floor. Determine the book’s potential energy relative to the floor. What is the book’s potential energy relative to the head of a 1.65 meter tall person?

4. A shot-putter heaves a 7.26 kg shot with a velocity of 7.5 m/s. Determine the kinetic energy of the shot. How much work was done on the shot to give it its kinetic energy?

5. Calculate the kinetic energy of a 750 kg compact car moving at 100 km/hr. How much work must be done to slow the car down to 50 km/hr?

6. Determine the mechanical energy of a 450 kg roller coaster moving at 30 m/s at the bottom of the first dip which is 15 meters above the ground.

7. Julie has a mass of 49 kg. What is her potential energy when standing on the 6 meter diving board? (She is 6 meters above the water.) Julie jumps off the diving board. What is her kinetic energy right before she hits the water? How fast does Julie hit the water?

8. An unfortunate skydiver’s parachute fails to open. If the diver hits the ground going 300 m/s, determine the height from which the ill-fated jump was make.

|9. |[pic] |

|Calculat| |

|e the | |

|potentia| |

|l, | |

|kinetic,| |

|and | |

|mechanic| |

|al | |

|energies| |

|, | |

|velocity| |

|, work, | |

|and | |

|power of| |

|the ball| |

|at the | |

|various | |

|location| |

|s. | |

Where did the term horsepower originate?

The term horsepower came from Scottish inventor James Watt. The value for a unit of horsepower was determined after Watt performed several experiments on horses pulling coal. He originally determined that the average horse was able to pull 22,000 foot-pounds every one minute. In other words, a horsepower was defined as the amount of power exerted to move 22,000 pounds of coal by one foot in one minute. Watt was not happy with his figure because he felt it was too low; he thought the average horse was more powerful than his original calculations and experiment indicated, so after extensive study of horses, he increased the value of a horsepower to 33,000 foot-pounds per minute. (1 HP = 746 W)

What countries are the largest consumers of energy?

The United States consumes over 28% more energy than it produces. That accounts for nearly a quarter of the energy consumed throughout the entire world, while the population of the United States accounts for only 5% of the world’s population.

Rank Country

1 United States

2 China

3 Russia

4 Japan

5 Germany

6 Canada

7 India

8 United Kingdom

9 France

10 Italy

What are the average yearly costs of some general home appliances?

Home climate control and appliances account for approximately one third of the energy consumption in the United States. The average cost for energy is approximately $0.12 per KwH (kilowatt-hour), but varies throughout the country. The following is a listing of home appliances, their typical usage, and the cost for one full year.

Appliance Energy (KwK) Annual Cost @ $0.12 / Kw

Television 1000 $120

(8 hours per day)

Stove with Oven 1000 $120

Washer 150 $18

Dryer 1000 $120

Refrigerator 1200 $152

Frost-free Refrigerator 2000 $240

Hot-water Heater 5000 $600

Window Air-conditioner 1500 $180

(if used year ‘round)

-----------------------

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M2

M1

(x = ? m

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M1 = 1 kg

M2 = 2 kg

h = 30m

dy

dx2

h

dy

dx

h

No basket necessary, do not let the ball hit the motion detector

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2. How many times would you have to climb the stairs to burn off your meal of choice?

htot

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htot

h

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