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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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Most popular questions from this chapter

Jorge is going to bungee jump from a bridge that is \(55.0 \mathrm{m}\) over the river below. The bungee cord has an unstretched length of \(27.0 \mathrm{m} .\) To be safe, the bungee cord should stop Jorge's fall when he is at least $2.00 \mathrm{m}\( above the river. If Jorge has a mass of \)75.0 \mathrm{kg},$ what is the minimum spring constant of the bungee cord?
The length of a spring increases by \(7.2 \mathrm{cm}\) from its relaxed length when a mass of \(1.4 \mathrm{kg}\) is hanging in equilibrium from the spring. (a) What is the spring constant? (b) How much elastic potential energy is stored in the spring? (c) A different mass is suspended and the spring length increases by \(12.2 \mathrm{cm}\) from its relaxed length to its new equilibrium position. What is the second mass?
(a) Calculate the change in potential energy of \(1 \mathrm{kg}\) of water as it passes over Niagara Falls (a vertical descent of \(50 \mathrm{m}\) ). (b) \(\mathrm{At}\) what rate is gravitational potential energy lost by the water of the Niagara River? The rate of flow is $5.5 \times 10^{6} \mathrm{kg} / \mathrm{s} .\( (c) If \)10 \%$ of this energy can be converted into electric energy, how many households would the electricity supply? (An average household uses an average electrical power of about \(1 \mathrm{kW} .\) )
Prove that \(U=-2 K\) for any gravitational circular orbit. [Hint: Use Newton's second law to relate the gravitational force to the acceleration required to maintain uniform circular motion.]
Two springs with spring constants \(k_{1}\) and \(k_{2}\) are connected in series. (a) What is the effective spring constant of the combination? (b) If a hanging object attached to the combination is displaced by \(4.0 \mathrm{cm}\) from the relaxed position, what is the potential energy stored in the spring for \(k_{1}=5.0 \mathrm{N} / \mathrm{cm}\) and $k_{2}=3.0 \mathrm{N} / \mathrm{cm} ?$ [See Problem \(83(\mathrm{a}) .]\)
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