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$\bullet$$\bullet$ A winch is used to drag a 375 $\mathrm{N}$ crate up a ramp at a con-stant speed of 75 $\mathrm{cm} / \mathrm{s}$ by means of a rope that pulls parallel tothe surface of the ramp. The rope slopes upward at $33^{\circ}$ abovethe horizontal, and the coefficient of kinetic friction between theramp and the crate is 0.25 . (a) What is the tension in the rope?(b) If the rope were suddenly to snap, what would be the accel-eration of the crate immediately after the rope broke?

a) 283 $\mathrm{N}$b) 7.39 $\mathrm{m} / \mathrm{s}^{2}$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

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question 45 is that a winch is used to drink 375 mutant. Create up a ramp at a constant speed at 75 centimetres per second by means of a rope that pulls parallel to the servers of the ramp. The rope slopes upward at 33 degrees above the horizontal, and the coefficient of connect friction between the ramp from the greatest 330.25 Part of the question asks, what is the tension of the rope and B? If the rope was suddenly to snap, what would be the celebration of the crate immediately after the book? This is their scenario here. First thing you should do is in the cage, our axes directions often simpler to leave our access X in the direction of the inclined plane. So we'll do that here. Part of his question, of course, that this is our box that's being pulled, the tension that pulls up to the right. So what? We should do a force body diagram on to see what forces are at play here soon that there's what you see, the weight pulls the objects street downward. There's a component of the weight in the y direction W Why which, if the crate is being angled at this single data, means this angle here is also data as a short of diagram, that means the y component of the weight based on the figure here, it's the coastline of the angle. So that's w co sign data and the weight converted, pointing down the ramp something in the X direction which would correspond to the value here, which, indeed, which means the X component will be, um, the wait times sign of data. There's no normal force pushing against the surface of the ramp, and since it's being pulled up, I'm sure there's tension in the rope. Which also means is a fiction for us acting opposing that motion so pretty. If you want to find the tension look of the forces in our X direction has to be zero because we're going to get a constant speed. Okay, so your attention protects, so leave a positive X direction. We have the wait time site data opposing it, and we have the force of kinetic friction. F k Equalling zero. So it is right are attention to be w side data plus F k, which is our kinetic friction well played by our normal where if we look at our forces in my direction down here, of course, it's not accelerating that directions. That has to be zero that's balanced by the normal force minus the y component of our weight, which is just w co sign there equals zero. So that means the normal force must equal that I can play that into my equation for attention. W sign Dina Hope, Sign data UK and the weight and Co sign. So looking are givens. We know the weight of the box. We know, um ukm enough data. So we have all our terms here, something some people again. So 3 75 which I pulled out in front because we term in both the times sign of 33 degrees plus coefficient 0.25 times co sign 33 degrees. So again, I pulled away to amounts of a singular 375 Newton term. And by applying this, we find that the tension in the rope must be 283. Nunes, Maybe if the root were to break, what were they thought it in the great be at at the time of, um, snap Ege, we can say so That scenario, our attention would be zero. But before that, all of attention would be a would be shifted into our force sledding down the ramp that equals and a so their attention, which are you taking to account, aren't force of friction. Can you represent it as just a sorry for us again, which is their attention? We have a value for attention. Whosoever acceleration. It could just be tension over mass who were not give the master given a weight, both attention for us, divided by the weight over G. And so since we captured attention to be to 83 that's what this top term here, the weight we know of three hairs every five mins and so we can calculate the acceleration down the ramp to be 7.39 meters per second squared. So in the statement, I really I probably should indicated that it will be negative because it's traveling in the negative X direction. That's why I mentioned it would be down the ramp, so I should have a negative term across all of these. I was trying in the negative X direction. So just start so clear and so chop up anything, make it too messy. It goes negative 7.39 meters per second.

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