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Chapter 6: Problem 4

The tension in the horizontal towrope pulling a waterskier is \(240 \mathrm{N}\) while the skier moves due west a distance of \(54 \mathrm{m}\). How much work does the towrope do on the water-skier?

Short Answer

Expert verified
Answer: The work done by the towrope on the water-skier is 12,960 Joules (J).

Step by step solution

01

Write down the given values

We are given: - Tension in the towrope (F): 240 N - Distance traveled by the skier (d): 54 m - Angle between the force vector and the displacement vector (theta): 0 degrees
02

Convert the angle to radians

Since cos function takes input in radians, we need to convert the angle theta from degrees to radians. theta = 0 degrees * (pi/180) = 0 radians
03

Apply the formula for work

Now, we can apply the formula for work: Work = F * d * cos(theta)
04

Calculate the work

Let's calculate the work done on the skier: Work = 240 N * 54 m * cos(0 radians) = 240 N * 54 m * 1 = 12960 N * m
05

Express the answer

The work done by the towrope on the water-skier is 12,960 Joules (J).

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