A sled and rider with a combined mass o 50kg are at the top of a hill a height o

Question

A sled and rider with a combined mass o 50kg are at the top of a hill a height of 8m above the level ground below. The sled is given a push providing an initial kinetic energy at the top of the hill of 900J.

A. Choosing a reference level at the bottom of the hill, What is the potential energy of the sled and rider at the top of the hill?

B. After the push, What is the total mechanical energy of the sled and rider at the top of the hill?

C. If friction can be ignored, What will be the kinetic energy of the sled and rider at the bottom of the hill?

Explanation / Answer

A) The potential energy of the sled and rider at the top of the hill is U = mgh = (50 kg)(9.8 m/s2 )(8 m) = 3920 J.

B) The total mechanical energy of the sled and rider at the top of the hill is E = K + U = 900 J + 3920 J = 4820 J.

C) Ignoring friction, the sled and rider should have the same mechanical energy at the bottom of the hill that they had at the top of the hill. However, at the bottom of the hill, this mechanical energy is in the form of kinetic energy, so E = K. Therefore, the sled and rider have 4820 J of kinetic energy at the bottom of the hill.

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