A water-skier is being pulled by a tow rope attached to a boat. As the driver pushes the throttle forward, the skier accelerates. A 83.9-kg water-skier has an initial speed of 6.3 m/s. Later, the speed increases to 10.1 m/s. Determine the work done by the net external force acting on the skier.
Would I use the equation
KEf-KE0 = 1/2mvf^2 - 1/2mv0^2 ?
work = change in Ke
= (1/2) m (V2^2 - V1^2)
so I did (1/2)(83.9)(10.1-6.3) and got 159.41 J.Is this correct?
Disregard question.
Yes, you are correct! To determine the work done by the net external force acting on the skier, you can use the equation you mentioned, which relates the initial and final kinetic energies.
The equation you mentioned is:
KE_final - KE_initial = 1/2 * m * vf^2 - 1/2 * m * v0^2
In this equation:
- KE_final represents the final kinetic energy, which is equal to (1/2) * m * vf^2, where m is the mass of the skier and vf is the final speed.
- KE_initial represents the initial kinetic energy, which is equal to (1/2) * m * v0^2, where v0 is the initial speed.
By substituting the given values, we can calculate the work done by the net external force.
Given:
m = 83.9 kg (mass of skier)
v0 = 6.3 m/s (initial speed)
vf = 10.1 m/s (final speed)
Let's substitute these values into the equation and calculate the work done:
KE_final - KE_initial = 1/2 * m * vf^2 - 1/2 * m * v0^2
KE_final = (1/2) * m * vf^2 = (1/2) * 83.9 kg * (10.1 m/s)^2 = 4245.42 Joules
KE_initial = (1/2) * m * v0^2 = (1/2) * 83.9 kg * (6.3 m/s)^2 = 1663.8695 Joules
Work done = KE_final - KE_initial = 4245.42 Joules - 1663.8695 Joules = 2581.55 Joules
Therefore, the work done by the net external force acting on the skier is 2581.55 Joules.