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Predict/Calculate A tow rope, parallel to the water, pulls a water skier directly behind the boat with constant velocity for a distance of 72 $\mathrm{m}$ before the skier falls. The tension in the rope is

140 $\mathrm{N}$ (a) Is the work done on the boat by the rope positive, negative, or zero? Explain. (b) Calculate the work done by the rope on the boat.

a) See the solution.

b) $W=-10080 \mathrm{J}$

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Cornell University

Numerade Educator

Simon Fraser University

Hope College

Okay, So a tow rope parallel to the water pulls a water skier directly behind the boat with constant velocity for a distance of 70 72 meters before the skier falls. Okay, so the tension in the rope is 140 Nunes. All right, so here is the tension in the rope. Okay. So, T t that's 140 Nunes. Okay, 140 newts. All right, we're asked. Is the work done on the boat by the rope? Okay, so here's where the rope in the boat touch. Right. Um, is the work done on the boat by the row? Positive or negative? Okay, well, check this out. The rope applies this force against the boat. Right? Because you can think of it as you know, you're dragging this skier on the on the water, and the water is basically providing this tension, you know, like, uh, the skiers putting the skis here. And yet, so the tension is created by by that friction, Essentially. All right. And at this point, you can see that the rope is pulling backward on the boat. Okay, so the force is in this direction, all right? And the displacement is in that direction, All right. And so we have that F Times X in this case is gonna be negative. E less than zero. All right. And what exactly is that? Ah, work. Okay, so how can we calculate that work? So this is a all right, eh? The answer should be negative. And b that work. It's simply the force. Okay, which is gonna be negative. 140 Nunes multiplied by the distance over which the skier travels before he falls. So 72 all right. And that is negative. 10,000 and 80 Jules.