The tension in the horizontal towrope pulling a water-skier is 266 N while the skier moves due west a distance of 53.5 m. How much work does the towrope do on the water-skier?
Question
The tension in the horizontal towrope pulling a water-skier is 266 N while the skier moves due west a distance of 53.5 m. How much work does the towrope do on the water-skier?
Solution
The work done by a force is given by the equation:
Work = Force x Distance x cos(θ)
where:
- Force is the magnitude of the force applied,
- Distance is the distance over which the force is applied, and
- θ is the angle between the force and the direction of motion.
In this case:
- The force (tension in the towrope) is 266 N,
- The distance (the skier moves) is 53.5 m, and
- The angle θ is 0 degrees because the force and the motion are in the same direction (due west).
So, we can substitute these values into the equation:
Work = 266 N x 53.5 m x cos(0)
Note that cos(0) = 1, so the equation simplifies to:
Work = 266 N x 53.5 m x 1
Therefore, the work done by the towrope on the water-skier is:
Work = 14231 Joules.
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