A girl and her bicycle have a total mass of 42 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 25 N,what is her speed at the bottom?

Question

Quizplus · Accepted Answer

Using the conservation of energy principle, the initial gravitational potential energy at the top of the hill is transformed into kinetic energy and work done against friction at the bottom of the hill.

Initial potential energy = mgh = 42 kg x 9.8 m/s^2 x 10 m = 4116 J

Final kinetic energy = (1/2)mv^2, where v is the unknown speed at the bottom
Final work done against friction = Fd = 25 N x 100 m = 2500 J

Since energy is conserved, we can equate the initial potential energy to the sum of kinetic energy and work done against friction:

Initial potential energy = Final kinetic energy + Work done against friction
4116 J = (1/2)mv^2 + 2500 J
Solving for v, we get:
v = sqrt[(4116 J - 2500 J) x 2 / 42 kg] = 10.1 m/s

Therefore, the girl's speed at the bottom of the hill is 10.1 m/s.

A Girl and Her Bicycle Have a Total Mass of 42