Two tugboats pull a disabled supertanker. Each tug exerts a const...

Question

Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.80×106N, one 14° west of north and the other 14° east of north, as they pull the tanker 0.75 km toward the north. What is the total work they do on the supertanker?

Accepted Answer

Hey everyone today, we're dealing with the problem about net force in a system or network in the system. So we're being told that we have a skater, this is our skater right here skater. This skater has been pulled by two different bikers, A distance of 30 m, he's been pulled 30 m on a flat road. Now each biker is exerting a different force on this skater. There is a first force A force heading west of 100 newtons. There's also a force to the north That is also 100 newtons applied by the 2nd biker. With this information. We're being asked to find the network. Now, if we recall For network, we need two quantities, we need the net force and we need the distance traveled. Well, we already have the distance traveled, it's simply 30 m 30 m. However, we still need the net force. Now we know that there are two different 100 Newton forces, but they're being applied in different directions. So how do we tackle this? Well, let me go back and just redraw our diagram a little neater. We have the West Force. I'll just write this is West and this is our North force North. Now, the interesting thing is they are both of equal magnitude, they're both 100 Newton forces. So the forces are equal equal in magnitude. So with that in mind, we can go ahead and realize that if we add up these two forces and remember we can add forces or add vectors by just adding the actual diagram vectors. If we're to add up these vectors, We can see that. The result in vector which will be the net force will be at an angle of data, which in this case will be 45°. So what does this mean exactly? Well, again, let us go through what we know. There are two For the net force. There are 2 100 Newton forces. And That net force creates a or the net force acting upon the skater forms a 45 degree angle with the horizontal, which means since it is in the horizontal direction. And if we are to consider this a excuse me? If we have to consider this a right triangle, if the resulting vector access our hypotenuse and this is our triangle. This is a hypotenuse, that's our angle theta. And this is the direction of travel. Then we're going to have to utilize our tree econometric functions because the direction of travel is adjacent to the angle itself. So with our econometric identities, we have so to oops tour when it is adjacent when the direction of travel or when the side in question is adjacent to the hypotenuse and the angle in question, we can use Kassian to go ahead and solve for it. So we'd have to multiply by cosine of theta Which is in this case cosign 45°. So that is our net force. So with all this in mind substituting back into our total network, we get that it is two times newtons Multiplied by Kassian 45° Multiplied by 30 m. We get a final answer Of 4,242.6 jewels, and that'll be the network done on the skater or answer choice. C. I hope this helps, and I look forward to seeing you all in the next one.

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