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 63.6-kg water-skier has an initial speed of 5.3 m/s. Later, the speed increases to 10.8 m/s. Determine the work done by the net external force acting on the skier.
I got +5630 J, and it was wrong. I'm not sure why, or how to do it correctly.
The NET external force is the tow line force minus friction.
The net force increases the kinetic energy, by an amount
(63.6/2)(10.8^2 - 5.3^2) = 2816 J
That is the work done by net force.
It looks like you used MV^2 for the kinetic energy instead of the correct (1/2)M*V^2.
Thank you! That's exactly what I did wrong. :)
To determine the work done by the net external force acting on the skier, you can use the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.
The change in kinetic energy (ΔKE) can be calculated as the final kinetic energy minus the initial kinetic energy:
ΔKE = KE_final - KE_initial
The formula for kinetic energy (KE) is:
KE = (1/2) * mass * velocity^2
Substituting the given values:
KE_initial = (1/2) * 63.6 kg * (5.3 m/s)^2
KE_final = (1/2) * 63.6 kg * (10.8 m/s)^2
Now you can find the change in kinetic energy:
ΔKE = (1/2) * 63.6 kg * (10.8 m/s)^2 - (1/2) * 63.6 kg * (5.3 m/s)^2
= (1/2) * 63.6 kg * (116.64 m^2/s^2) - (1/2) * 63.6 kg * (28.09 m^2/s^2)
= (1/2) * 63.6 kg * (116.64 - 28.09) m^2/s^2
= (1/2) * 63.6 kg * (88.55) m^2/s^2
= 2831.46 J
Therefore, the work done by the net external force acting on the skier is 2831.46 J, not +5630 J.
To determine the work done by the net external force acting on the skier, we need to calculate the change in kinetic energy of the skier.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:
Work = ΔKE
ΔKE = KE_final - KE_initial
Given that the skier has an initial speed (KE_initial) of 5.3 m/s and a final speed (KE_final) of 10.8 m/s, we can calculate the change in kinetic energy (ΔKE).
ΔKE = 0.5 * m * (v_final^2 - v_initial^2)
where m is the mass of the skier. In this case, m = 63.6 kg, v_initial = 5.3 m/s, and v_final = 10.8 m/s.
Let's calculate ΔKE:
ΔKE = 0.5 * 63.6 kg * (10.8 m/s)^2 - 0.5 * 63.6 kg * (5.3 m/s)^2
ΔKE = 0.5 * 63.6 kg * (116.64 m^2/s^2) - 0.5 * 63.6 kg * (28.09 m^2/s^2)
ΔKE = 3735.1872 J - 897.3344 J
ΔKE = 2837.8528 J
Therefore, the work done by the net external force acting on the skier is 2837.8528 J.
It appears that your calculation was incorrect. Please double-check your math and ensure that you square both the initial and final velocities before multiplying them by the mass and other terms.