A ski trail makes a vertical descent of 77 m. A novice skier, unable to control his speed, skis down this trail and is lucky enough not to hit any trees.
If the skier is moving at 17 m/s at the bottom of the trail, calculate the total work done by friction and air resistance during the run. The skier's mass is 74 kg.
KJ?
I don't undertand how to do this am confused :/ please help!
To calculate the total work done by friction and air resistance during the skier's run, we need to first calculate the change in the skier's kinetic energy.
The change in kinetic energy (ΔKE) is given by the equation:
ΔKE = KE_final - KE_initial
In this case, the skier's initial kinetic energy (KE_initial) is equal to (1/2) * m * v^2, where m is the skier's mass and v is the skier's initial velocity.
KE_initial = (1/2) * m * v^2
KE_initial = (1/2) * 74 kg * (17 m/s)^2
KE_initial = 8812 J
The skier's final kinetic energy (KE_final) is also equal to (1/2) * m * v^2, but with the skier's final velocity (v) instead.
KE_final = (1/2) * 74 kg * (0 m/s)^2
KE_final = 0 J
The change in kinetic energy (ΔKE) is equal to:
ΔKE = KE_final - KE_initial
ΔKE = 0 J - 8812 J
ΔKE = -8812 J
Since the change in kinetic energy is negative, there must be an external force doing negative work on the skier. This external force is the combined work done by friction and air resistance.
Therefore, the total work done by friction and air resistance is equal to the change in kinetic energy:
Work = ΔKE
Work = -8812 J
Therefore, the total work done by friction and air resistance during the skier's run is -8812 J.