A boy in a wheelchair (total mass, 46.9kg) wins a race with a skateboarder. He has a speed of 1.30m/s at the crest of a slope 2.35m high and 12.6m long. At the bottom of the slope, his speed is 6.28m/s. If air resistance and rolling resistance can be modeled as a constant frictional force of 41.3N, calculate the work he did in pushing forward on his wheels during the downhill ride.
work done:
gain in energy=mgh+initial KE-final KE
friction energy=41.3*12.5
work he did: friction energy-gain in energy
To calculate the work done by the boy in pushing forward on his wheels during the downhill ride, we need to consider the change in kinetic energy.
Work (W) is defined as the change in kinetic energy (ΔKE) of an object. Mathematically, it can be expressed as:
W = ΔKE
The change in kinetic energy can be calculated by subtracting the initial kinetic energy (KEi) from the final kinetic energy (KEf):
ΔKE = KEf - KEi
We can find the initial kinetic energy using the given mass (m) and initial speed (vi):
KEi = (1/2) * m * vi^2
Similarly, we can find the final kinetic energy using the given mass (m) and final speed (vf):
KEf = (1/2) * m * vf^2
Next, let's calculate the initial and final kinetic energies:
KEi = (1/2) * 46.9 kg * (1.30 m/s)^2
KEi = 38.633 J
KEf = (1/2) * 46.9 kg * (6.28 m/s)^2
KEf = 893.667 J
Now, we can find the change in kinetic energy:
ΔKE = KEf - KEi
ΔKE = 893.667 J - 38.633 J
ΔKE = 855.034 J
Since work is equal to the change in kinetic energy, the work done by the boy in pushing forward on his wheels during the downhill ride is 855.034 Joules.