A boy on a bicycle is resting at the top of a hill. Then, he rides his bicycle
down the hill. Describe how the boy’s potential and kinetic energy differ at the
top, middle, and bottom of the hill.

Top: PE = max, KE = 0

Middle: PE = half, KE = half

Bottom: PE = 0, KE = max

Explanation:

The potential energy of an object is the energy possessed by the object due to its location; it is given by

where

m is the mass of the object

g is the acceleration due to gravity

h is the height of the object from the ground

The kinetic energy of an object is the energy possessed by the object due to its motion; it is given by

where

v is the speed of the object

Now we analyze the three situations for the boy on the bycicle:

Top of the hill: here h (the height) is maximum, so the potential energy is maximum, while the speed is zero, therefore the kinetic energy is zero.

Middle of the hill: here h (the height) is half of the initial value, therefore the potential energy is also half of the initial potential energy. According to the law of conservation of energy, the total mechanical energy (potential+kinetic) is constant: this means that also the kinetic energy is half of the initial potential energy.

Bottom of the hill: here h is zero, therefore the potential energy is now zero. As a result, all the mechanical energy has been converted into kinetic energy, therefore the kinetic energy is maximum and it is equal to the potential energy of the boy when he was at the top.

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