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 10.0 m high and 100 m long.How much kinetic energy and potential energy is lost to friction?

Question

Quizplus · Accepted Answer

Initial potential energy = mgh = 40.0 kg x 9.8 m/s^2 x 10.0 m = 3 920 J
Initial kinetic energy = 0.5 x 40.0 kg x (5.0 m/s)^2 = 500 J

Final potential energy = mgh = 40.0 kg x 9.8 m/s^2 x 0 m = 0 J
Final kinetic energy = 0.5 x 40.0 kg x (2 x 5.0 m/s)^2 = 2 000 J

The total mechanical energy lost to friction is the difference between the initial mechanical energy and the final mechanical energy:
ΔE = (initial potential energy + initial kinetic energy) - (final potential energy + final kinetic energy)
ΔE = (3 920 J + 500 J) - (0 J + 2 000 J)
ΔE = 2 420 J

Therefore, the answer is (A) 2 420 J.

A Girl and Her Bicycle Have a Total Mass of 40.0