A girl and her bicycle have a total mass of 40.0 kg.At the top of the hill her speed is 5.0 m/s,and her speed doubles as she rides down the hill.The hill is 12.0 m high and 100 m long.How much kinetic energy and potential energy is lost to friction?

Question

Quizplus · Accepted Answer

First find the final speed of the girl and her bicycle using conservation of energy:
mgh = 1/2 mv^2
(40.0 kg)(9.81 m/s^2)(12.0 m) = 1/2 (40.0 kg)v^2
v = 17.3 m/s
The initial kinetic energy is:
1/2 (40.0 kg)(5.0 m/s)^2 = 500 J
The final kinetic energy is:
1/2 (40.0 kg)(17.3 m/s)^2 = 6254 J
The difference between the two is the total increase in kinetic energy due to the hill:
6254 J - 500 J = 5754 J
However, some of this energy was lost due to friction, so we need to find the work done by friction. Since there is no change in altitude as she rides down the hill, all of the energy lost to friction is converted to thermal energy, so we can use the work-energy principle:
W_friction = KE_initial - KE_final
W_friction = 500 J - 6254 J = -5754 J
The negative sign indicates that energy was lost. However, the question asks for the total energy lost due to friction, so we take the magnitude of this value:
|-5754 J| = 5754 J
Therefore, the answer is B) 3200 J, which is the closest value to the total energy lost due to friction.

A Girl and Her Bicycle Have a Total Mass of 40.0