A boy in a wheelchair (total mass 56.5 kg) has speed 1.40 m/s at the crest of a slope 2.05 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.
Question
Answer: 439.01 J
Explanation:
The Kinetic Energy at the top + Potential Energy at the top + Work Done = Kinetic Energy at the bottom + Friction loss
1/2mv² + mgh + W = 1/2 mv² + Fd
1/2 * 56.5 * (1.4)² + 56.5 * 9.8 * 2.05 + W = 1/2 * 56.5 * (6.3)² + 41 * 12.4
1/2 * 56.5 * 1.96 + 56.5 * 9.8 * 2.05 + W = 1/2 * 56.5 * 39.69 + 41 * 12.4
55.47 + 1135.085 + W = 1121.243 + 508.4
1190.555 + W = 1629.643
W = 1629.643 – 1190.555
W = 439.088
W = 439.09 J