# Problem: Jonathan is riding a bicycle and encounters a hill of height h. At the base of the hill, he is traveling at a speed vi . When he reaches the top of the hill, he is traveling at a speed vf . Jonathan and his bicycle together have a mass m. Ignore friction in the bicycle mechanism and between the bicycle tires and the road. (a) What is the total external work done on the system of Jonathan and the bicycle between the time he starts up the hill and the time he reaches the top? (b) What is the change in potential energy stored in Jonathan’s body during this process? (c) How much work does Jonathan do on the bicycle pedals within the Jonathan– bicycle–Earth system during this process?

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###### Problem Details

Jonathan is riding a bicycle and encounters a hill of height h. At the base of the hill, he is traveling at a speed vi . When he reaches the top of the hill, he is traveling at a speed vf . Jonathan and his bicycle together have a mass m. Ignore friction in the bicycle mechanism and between the bicycle tires and the road.

(a) What is the total external work done on the system of Jonathan and the bicycle between the time he starts up the hill and the time he reaches the top?
(b) What is the change in potential energy stored in Jonathan’s body during this process?
(c) How much work does Jonathan do on the bicycle pedals within the Jonathan– bicycle–Earth system during this process?