A boy in a wheelchair (total mass, 46.0kg) wins a race with a skateboarder. He has a speed of 1.33m/s at the crest of a slope 2.24m high and 13.2m long. At the bottom of the slope, his speed is 6.35m/s. If air resistance and rolling resistance can be modeled as a constant frictional force of 42.1N, calculate the work he did in pushing forward on his wheels during the downhill ride.
jhk
To calculate the work done by the boy in pushing forward on his wheels during the downhill ride, we can use the work-energy principle. The work done is equal to the change in kinetic energy.
The initial kinetic energy of the boy at the crest of the slope is given by:
KE_initial = (1/2) * m * v_initial^2
The final kinetic energy of the boy at the bottom of the slope is given by:
KE_final = (1/2) * m * v_final^2
The change in kinetic energy is then given by:
ΔKE = KE_final - KE_initial
However, we also need to take into account the work done against the frictional force. The work done against friction is given by the formula:
Work_friction = F_friction * d
where F_friction is the frictional force and d is the distance the boy traveled.
Now, let's calculate the values step by step:
1. Calculate the initial kinetic energy:
KE_initial = (1/2) * 46.0kg * (1.33m/s)^2
2. Calculate the final kinetic energy:
KE_final = (1/2) * 46.0kg * (6.35m/s)^2
3. Calculate the change in kinetic energy:
ΔKE = KE_final - KE_initial
4. Calculate the work done against friction:
Work_friction = 42.1N * 13.2m
5. Calculate the total work done:
Total work = ΔKE + Work_friction
Substitute the values into the formulas and calculate the final result.