5-2 Energy. Potential and Kinetic Energy. Energy: The ability to do work. Vocabulary

Transcription

1 5-2 Energy Potential and Kinetic Energy Vocabulary Energy: The ability to do work. There are many dierent types o energy. This chapter will ocus on only mechanical energy, or the energy related to position (potential energy) and motion (kinetic energy). Vocabulary Potential Energy: Energy o position, or stored energy. 66 Energy and Machines An object gains gravitational potential energy when it is lited rom one level to a higher level. Thereore, we generally reer to the change in potential energy or PE, which is proportional to the change in height, h.

2 gravitational potential energy (mass)(acceleration due to gravity)( height) or PE mgh It is important to remember that gravitational potential energy relies only upon the vertical change in height, h, and not upon the path taken. In addition to gravitational potential energy, there are other orms o stored energy. For example, when a bow is pulled back and beore it is released, the energy in the bow is equal to the work done to deorm it. This stored or potential energy is written as PE Fd. Springs possess elastic potential energy when they are displaced rom the equilibrium position. The equation or elastic potential energy will not be used in this chapter. Vocabulary Kinetic Energy: Energy o motion. The kinetic energy o an object varies with the square o the speed. kinetic energy a (mass)(speed) 2 or KE a mv 2 The SI unit or energy is the joule. Notice that this is the same unit used or work. When work is done on an object, energy is transormed rom one orm to another. The sum o the changes in potential, kinetic, and heat energy is equal to the work done on the object. Mechanical energy is transormed into heat energy when work is done to overcome riction. Conservation o Energy According to the law o conservation o energy, energy cannot be created or destroyed. The total amount o mechanical energy in a system remains constant i no work is done by any orce other than gravity. In an isolated system where there are no mechanical energy losses due to riction KE PE In other words, all the kinetic and potential energy beore an interaction equals all the kinetic and potential energy ater the interaction. KE o PE o KE PE or a mv 2 o mgh o a mv 2 mgh As a reminder, the terms with the subscript o are the initial conditions, while those with the subscript are inal conditions. Energy and Machines 67

3 Solved Examples Example 4: Legend has it that Isaac Newton discovered gravity when an apple ell rom a tree and hit him on the head. I a 0.20-kg apple ell 7.0 m beore hitting Newton, what was its change in PE during the all? Solution: For a given object, the change in PE depends only upon the change in position. The apple does not need to all all the way to the ground to experience an energy change. Given: m 0.20 kg Unknown: PE? g 0.0 m/s 2 Original equation: PE mgh h 7.0 m Solve: PE mgh (0.20 kg)(0.0 m/s 2 )(7.0 m) 4 J Example 5: Agreyhound at a race track can run at a speed o 6.0 m/s. What is the KE o a 20.0-kg greyhound as it crosses the inish line? Given: m 20.0 kg Unknown: KE? v 6.0 m/s Original equation: KE a mv 2 Solve: KE a mv 2 a (20.0 kg)(6.0 m/s) J Example 6: In a wild shot, Bo lings a pool ball o mass m o a 0.68-m-high pool table, and the ball hits the loor with a speed o 6.0 m/s. How ast was the ball moving when it let the pool table? (Use the law o conservation o energy.) Given: v 6.0 m/s Unknown: v o? g 0.0 m/s 2 Original equation: KE PE h o 0.68 m h 0 m Solve: KE o PE o KE PE or a mv 2 o mgh o a mv 2 mgh Notice that mass is contained in each o these equations. Thereore, it cancels out and does not need to be included in the calculation. a a v 2 gh gh mv 2 mgh mgh o o v o a b m b 2 b a 6.0 m>s m>s 2 20 m2 0.0 m>s m2 8 m 2 >s m 2 >s m/s R 2 68 Energy and Machines 2

4 Example 7: Frank, a San Francisco hot dog vender, has allen asleep on the job. When an earthquake strikes, his 300-kg hot-dog cart rolls down Nob Hill and reaches point A at a speed o 8.00 m/s. How ast is the hot-dog cart going at point B when Frank inally wakes up and starts to run ater it? Solution: Because mass is contained in each o these equations, it cancels out and does not need to be included in the calculation. Also, the inclination o the hill makes no dierence. All that matters is the change in height. Given: v o 8.00 m/s Unknown: v? g 0.0 m/s 2 Original equation: KE PE h o 50.0 m h 30.0 m Solve: KE o PE o KE PE or a mv 2 o mgh o a mv 2 mgh a a v o 2 gh o gh mv o 2 mgh o mgh v a b m b 2 b R a 8.00 m>s m>s m2 0.0 m>s m m 2 >s m 2 >s m 2 >s m 2 >s m/s Energy and Machines 69

5 Practice Exercises Exercise 5: It is said that Galileo dropped objects o the Leaning Tower o Pisa to determine whether heavy or light objects all aster. I Galileo had dropped a 5.0-kg cannon ball to the ground rom a height o 2 m, what would have been the change in PE o the cannon ball? Exercise 6: The 2000 Belmont Stakes winner, Commendable, ran the horse race at an average speed o 5.98 m/s. I Commendable and jockey Pat Day had a combined mass o kg, what was their KE as they crossed the inish line? Exercise 7: Brittany is changing the tire o her car on a steep hill 20.0 m high. She trips and drops the 0.0-kg spare tire, which rolls down the hill with an initial speed o 2.00 m/s. What is the speed o the tire at the top o the next hill, which is 5.00 m high? (Ignore the eects o rotation KE and riction.) 2v o 2 2gh o h m>s m>s m m24 70 Energy and Machines

6 Exercise 8: AMexican jumping bean jumps with the aid o a small worm that lives inside the bean. a) I a bean o mass 2.0 g jumps.0 cm rom your hand into the air, how much potential energy has it gained in reaching its highest point. b) What is its speed as the bean lands back in the palm o your hand? 22 PE>m J2 > kg2 a. b. Exercise 9: A500.-kg pig is standing at the top o a muddy hill on a rainy day. The hill is 00.0 m long with a vertical drop o 30.0 m. The pig slips and begins to slide down the hill. What is the pig s speed at the bottom o the hill? Use the law o conservation o energy. 22g h m>s m2 Exercise 0: While on the moon, the Apollo astronauts enjoyed the eects o a gravity much smaller than that on Earth. I Neil Armstrong jumped up on the moon with an initial speed o.5 m/s to a height o m, what amount o gravitational acceleration did he experience? a a Energy and Machines 7

7 J m/s m/s