Question

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?

Answer 1

TheThe  potential energy will be

 ∆U → (1/2mvi²-1/2mvf²) -mgh-mgh .

What do you mean by potential  energy and why it is called potential?

Potential energy is energy stored that depends upon the relative position of various parts of a system. Any object that is lifted from its resting position has stored energy therefore it is called potential energy because it has a potential to do work when released.

Mass of system = m

Initial Velocity = vi

Final velocity = Vf

 Yi = 0, Yf = h

Now , total work done on system is,

Wg = Fgh

here , Fg = mg

 Wg = mgh

Now , potential energy is converted into kinetic energy .

∆ U = -(∆K+ ∆U)

∆U = (1/2mVi²-1/2mVf²) -mgh

To learn more about Potential energy click here

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