A girl and her bicycle have a total mass of 40 kg.At the top of the hill her speed is 5.0 m/s.The hill is 10 m high and 100 m long.If the force of friction as she rides down the hill is 20 N,what is her speed at the bottom?

Question

Quizplus · Accepted Answer

The initial potential energy of the girl and her bicycle at the top of the hill is given by:
PE1 = mgh = 40 kg × 9.81 m/s² × 10 m = 3,924 J

This potential energy is converted into kinetic energy at the bottom of the hill, where the speed of the girl and her bicycle is maximum. The final kinetic energy is given by:
KE2 = (1/2)mv²

The loss of energy due to friction along the way is given by:
ΔE = Wfriction = Ffriction × d = 20 N × 100 m = 2,000 J

Therefore, the final kinetic energy can be found by subtracting the loss of energy due to friction from the initial potential energy:
KE2 = PE1 - ΔE = 3,924 J - 2,000 J = 1,924 J

Solving for the final velocity v yields:
KE2 = (1/2)mv²
1,924 J = (1/2)(40 kg)v²
v = sqrt(2 × 1,924 J / 40 kg) = 10.9 m/s ≈ 11 m/s

Therefore, the answer is C)11 m/s.

A Girl and Her Bicycle Have a Total Mass of 40