a-worker-moves-a-30-mathrmkg-box-by-pulling-on-it-with-a-rope-that-makes-a-60circ-angle-with-the-hor

Question

A worker moves a 30 $\mathrm{kg}$ box by pulling on it with a rope that makes a $60^{\circ}$ angle with the horizontal. If the worker applies a force of 40 $\mathrm{N}$ and pulls the box over a distance of $20 \mathrm{m},$ how much work did the worker do?
(A) 100 $\mathrm{J}$
(B) 200 $\mathrm{J}$
(C) 400 $\mathrm{J}$
(D) 800 $\mathrm{J}$

Sachin Rao · Accepted Answer

a worker moves are 30 kg box by pulling on it with a rope that makes 60 anger 60 degree angle with the horizontal support this is a box and this is angle 60 degrees with the horizontal mass of this box is 30 kg. If the worker applies a force of 14, Newton Force is equal to 14. You 10 and pulls the works over a distance of 20 m. Right? How much work did the worker do? So we have to find them who have them. So we know that wagon is equal to F dot s director f not s. So this is equal to forces 14 into court 16 The direction of displacement and displacement is given 20 m. So this is equal to 14 to 20. That means 802 cost 60. So the work done by the worker is equal to 800. Multiply with cost 60. This is equal to 400 jewels. So the work done is 400 jewels. If you check our options also see we&#x27;ll be right. Option. Right. So this is the answer. Thank you.

Salamat Ali · Answer

worked and to take the box at the distance off 20 meter, making an angle force with the displacement. This is a force, and this is a box. We have heard this angle making 60 degrees. This is a displacement. Work is written is if if the cost, that up goals. So, um, force we have is a 40 Newton making a displacement off 20 meter with an angle off 60 degrees for 60 on This gives us the work off 400 jewels pulling their jewels. So the option C is the right answer.

Ankit Gupta · Answer

world in W is equal toe effect er dot product with a B veteran that is equal to 60 multiplied by 20 multiplied by cause off 38 degree minus 12 dignity that is equal to 1200 multiplied by course, off 26 degree that is approximately equal to 1079 foot pound. It means work Island is equal to 1079. £4.

Salamat Ali · Answer

work done by gravity on the box is given by Delta U Delta. You changing potential energy off the box. That is a minus. N g um, So final height, minus initial height. So the height we have here is ah, 10 meters. Great. Additional insulation is a 10 or a mosque. We have six kg. So multiplying. All these numbers use us. They work done by the gravity is a minus 600 jewels. Option B is the right answer.

Lili Schantz · Answer

for this problem. We want to find how much work is done pulling the box 25 feet along the ramp that is inclined at 10 degrees from the horizontal with a rope that forms an angle of 33 degrees to the horizontal and a force of £80. So we first seem to find Earth data because we know that work equals, um the magnitude of force times the magnitude of our distance. Times co sign data in the data is gonna be our angle between vectors. So we have this 10 degrees of our incline, and then we have the 33 degrees of the rope. So to find data, we want to find this angle here. And to do that, we need to do 33 minus 10 which is 23 degrees. So our data is 23. So now we can just plug everything and so we have work is 80 times 25 times co sign 23 degrees in that equals 1841 foot pounds.

Ben Nicholson · Answer

problem. 7.3. We have a mailbag with mess of 90 kilograms and on a length, a length of rope that&#x27;s three and 1/2 meters long. And then we&#x27;re supposed to imagine that a postal worker not shown here ah comes and pushes this over displacing at two meters horizontally, which means it also has a vertical displacement. Because it&#x27;s the rope is kept top, it&#x27;s obvious as to move along the circumference of a circle. Then we have some questions we&#x27;d like to answer about this situation other than presumably why they&#x27;re doing this. Um, So what is the force that the postal worker is having to exert on the bag horizontally to hold it in this position? And then what work is done by the row and the postal worker? And is it repositioning the bag up here? So a few things that we would, uh, probably find useful here, Um, one of them is this angle fader. Now we have opposite and iPod news sides of this triangle, so using the sign is the most convenient. So opposite over the news and then that gives this angle is 34 185 The greens which we can compute the lengths of these two sections here. One is the height here, and then the other is the actual distance that the thing moved vertically. So let&#x27;s call this one delta y, and that&#x27;s going to be equal to 0.6 to 8 meters, then the other one I don&#x27;t actually need. But you couldn&#x27;t find this problem. You find this by finding what this length is, and that&#x27;s attracting it from three and 1/2 meters. So you need to know what this is for the intermediate step. In any event, let&#x27;s not turn our attention. Two are questions here. So in order to figure out what the forces here, you know your first step in doing this type of thing is to draw a free body diagram. So this is our mailbag. There&#x27;s going to be the horizontal horizontal force that the, uh, the postal worker is is applying. And then there&#x27;s going to be a force of tension in the row which has the components Chico Science Data NT Science data. So, since the bag is not accelerating, you know some of the vertical forces has to eat zero. Oh, I&#x27;m sorry. and then also because this back is somewhere on Earth or some other planet. There&#x27;s also its weight. That&#x27;s that&#x27;s important. Yeah. Where was it? Yes, so supplies the magnitude of the tension times. The coastline of the angle is equal to the weight and the sum of the ex forces equaling zero implies that this force were interested in which, maybe a little confusing. But I called it F sub X beginning. So let&#x27;s continue. Um, this has to be equal to t sign. So now we have teas in both of these equations that we don&#x27;t really care about, But we can solve each one for tea and set them equal. So in this case, he is going to be equal to M G over Coast Bank data. At this case, he is going to be equal to the number. The thing we&#x27;re interested in, F sub x divided by a sign of fate. So f sub x equals m g times sign over coastline is tangent, then evaluated that we find that this has to be 600 10 cool. So it&#x27;s open up. Well, it&#x27;s a new thing here. So now we want to know what work. We want to know what work is done by the rope. As this bag is moving, however, recall that worked is the integral of the dot product of a forest along the path that it&#x27;s, you know, moving something. So here the displacements air all tangential to the circle that this is traveling around on, and the force of the tension in the robe is radio. And so they&#x27;re always at right angles, angles to each other. And so the dot product of to perpendicular vectors is always zero. So the rope is not doing anywhere. Well, how much work does the post office worker have to do? We know because of the work kinetic energy, the&#x27;re, um that since it&#x27;s at rest, that total work done is zero. Which means that we have work done by the postal worker has to be equal to the negative or make the negative of the work done by gravity. And we&#x27;re going to evaluate this than it&#x27;s sort of a mess because the we saw before Well, so we have to do this integral. So integrate the work done along the path as we saw before run, but sorry, a CZ we saw before he over here, The, uh, forced the postal workers exerting has a tangent of this angle that it&#x27;s going through. And it be. However, we know that the work done by gravity is the change in change and the gravitational potential Energy. This is negative, M. E. Um, there is change the opposite. Oh, yeah. I&#x27;m sorry to change in potential gravitational potential. Energy is the negative of the work done by gravity because gravity does negative work when you love something off. But it&#x27;s increasing its potential energy anyway. So, you know, from the previous page, I said that the change in height is went 6 to 8 meters of work postal worker does, which is equal to the change in potential energy of the bag. Just But, uh, these things in we know all of them is 550. Jules

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