A child of mass 30 kg rides a lightweight sled of negligible mass up a snowy hill…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
A child of mass 30 kg rides a lightweight sled of negligible mass up a snowy hill that is inclined at 15° above the horizontal. A friend pulls the child and sled up the 10 m long incline by exerting a constant 120 N force on a rope that is directed 20° above the surface of the incline. The coefficient of kinetic friction between the sled and snow is 0.10. After reaching the top, the child releases the rope and coasts back down to the bottom along the same path without additional pushing. Air resistance is negligible.
(1) Compute the work done on the child–sled system by the friend’s pulling force during the ascent.
(2) Compute the work done on the system by the gravitational force during the ascent.
(3) Compute the work done on the system by kinetic friction during the ascent, indicating its sign.
(4) Using your results, determine the net work done on the system during the ascent and state whether the child reaches the top moving faster, slower, or at the same speed compared with the speed at the bottom. Justify your answer qualitatively.
(5) During the descent, calculate the work done by gravity and by kinetic friction and determine the net work. Using the work–energy relationship, explain whether the child returns to the bottom with a speed equal to, greater than, or less than the initial speed at the start of the ascent.