Boy in a wheelchair (total mass 52.0 kg) has speed 1.40 m/s at the crest of a slope 2.35 m high and 12.4 m long. At the bottom of the slope his speed is 6.30 m/s. Assume air resistance and rolling resistance can be modeled as a constant friction force of 41.0 N. Find the work he did in pushing forward on his wheels during the downhill ride.

290.6J

Explanation:

According to the law of energy conservation, the work he did in pushing forward on his wheels and the work produced by friction during the downhill ride can be equal to the change of mechanical energy between the top and the bottom of the slope.

Let g = 9.81 m/s2

Let the bottom of the slope be ground 0 for his potential energy, then his potential energy at the top height h = 2.35 m of the slope would be

His kinetic energy at the top of the slope is

His kinetic energy at the bottom of the slope would be

The work done by friction F = 41N over distance of s = 12.4m is

Therefore we can apply the law of energy conservation