Question

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

Answer 1

The kinetic energy and potential energy lost to friction is 2,420 J.

Step-by-step explanation:

Given;

total mass, m = 40 kg

initial velocity of the girl, Vi = 5 m/s

hight of the hill, h = 10 m

length of the hill, L = 100 m

initial kinetic energy of the girl at the top hill:

`K.E_(i) = (1)/(2) mv_i^2 = (1)/(2) * 40 * (5)^2\\\\K.E_(i) = 500 \ J`

initial potential energy of the girl at the top hill:

`P.E_(i) = mgh_i = 40 * 9.8 * 10\\\\P.E_(i)= 3920 \ J`

Total energy at the top of the hill:

E = 500 J + 3920 J

E = 4,420 J

At the bottom of the hill:

final velocity = double of the initial velocity = 2 x 5 m/s = 10 m/s

hight of the hill = 0

final kinetic energy of the girl at the bottom of the hill:

`K.E_(f) = (1)/(2) mv_f^2 \\\\K.E_f = (1)/(2) * 40 * (10)^2 = 200 0 \ J`

final potential energy of the girl at the bottom of the hill:

`P.E_f = mgh_f = 40 * 9.8 * 0 = 0`

Based on the principle of conservation of energy;

the sum of the energy at the top hill = sum of the energy at the bottom hill

The energy at the bottom hill is less due to energy lost to friction.

`E_(friction) \ + E_(bottom)= E_(top)\\\\E_(friction) = E_(top) - E_(bottom)\\\\E_(friction) = 4,420 \ J - 2,000 \ J\\\\E_(friction) = 2,420 \ J`

Therefore, the kinetic energy and potential energy lost to friction is 2,420 J.