Question

A boy in a wheelchair (total mass 56.0 kg) has speed 1.40 m/s at the crest of a slope 2.30 m high and 12.4 m long. At the bottom of the slope his speed is 6.40 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.

Answer 1

Answer:

338.16 J

Explanation:

We are given that

Total mass ,m=56 kg

$v_0=1.4 m/s$

$h=2.3 m$

$l=12.4 m$

$v=6.4 m/s$

Friction force,f=41 N

We have to find the work done by boy in pushing the forward on his wheels during the downhill ride.

According to law of conservation of energy

$\frac{1}{2}mv^2_0+mgh+W=\frac{1}{2}mv^2+W_f$

$W=\frac{1}{2}mv^2+W_f-\frac{1}{2}mv^2_0-mgh$

$W=\frac{1}{2}m(v^2-v^2_0)+fl-mgh$

Where g=$9.8 m/s^2$

$W=\frac{1}{2}(56)((6.4)^2-(1.4)^2)+41(12.4)-56\times 9.8\times 2.3$

$W=338.16 J$