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You coast up a hill on your bicycle with decreasing speed.

Chapter 8, Problem 38P

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QUESTION:

Problem 38P

You coast up a hill on your bicycle with decreasing speed. Your friend pedals up the hill with constant speed. (a) Ignoring friction, does the mechanical energy of the you-bike-Earth system increase, decrease, or stay the same? Explain. (b) Does the mechanical energy of the friend-bike-Earth system increase, decrease, or stay the same? Explain.

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QUESTION:

Problem 38P

You coast up a hill on your bicycle with decreasing speed. Your friend pedals up the hill with constant speed. (a) Ignoring friction, does the mechanical energy of the you-bike-Earth system increase, decrease, or stay the same? Explain. (b) Does the mechanical energy of the friend-bike-Earth system increase, decrease, or stay the same? Explain.

ANSWER:

Part (a)

Step 1 of 2:

You are riding a bicycle with decreasing speed on a hill. Assume that the effects of friction can be ignored. We are going to find the change in the mechanical energy of your bike and the Earth system. There are no forces acting on the system.  

When you coast up with decreasing speed, the kinetic energy of the bicycle decreases but still you are moving up with the respect to the ground and the gravitational potential energy increases. Hence the total energy of the system remains the same as the kinetic energy is being converted into potential energy.

Answer: stays the same.

Part (b)

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