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$\bullet$$\bullet$ A $1130-\mathrm{kg}$ car is held in place by a light cable on a verysmooth (frictionless) ramp, as shown in Fig. 5.39 . The cablemakes an angle of $31.0^{\circ}$ above the surface of the ramp, and theramp itself rises at $25.0^{\circ}$ above the horizontal. (a) Draw a free-body diagram for the car. (b) Find the tension in the cable.(c) How hard does the surface of the ramp push on the car?

diagram5460 $\mathrm{N}$7220 $\mathrm{N}$

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 Washington

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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all right. A car that is all I'm inclined to think. Pulled up by cable at 31 degrees? No, from for that makes a 31 degree angle wet. The incline. Okay, the incline itself is 25. Okay, so let's start with the free body. Died burn part. And so you have obviously force of force of gravity. You wait acting downwards, and then you have a certain of so that's acting downwards. And you have attention from the cable acting upwards. And this is at an angle of 31 degrees from the incline. So there's an angle off the angle of 25 degrees here because that's the angle. A. That's how inclined the ramp is 25 degree angle between the vertical axis that we just nowhere setting up. Let me try out a little better, but essentially an angle. Uh, essentially, huh? The vertical axis. You should be bad access, Okay? And so the normal force is acting house on the car from off by the Ram. And so that's acting directly. That's hacking vertically, upwards. And okay, so those the convention we chose here is is that the X and Y axes are sort of like that? Not exactly, but that's where they are so inclined. Okay, They're not done. Traditional accent. Why? Like that? Somewhere he used to, anyway, So that s o. This free body diagram has a attention 31 degrees from the inclined. Now from the exactness ray and then normal force directly, vertically. And then the force of gravity is 25 degrees below the are at an angle of 25 degrees from the vertical access. Okay, so this is the real body diagrams. Slightly complicated, but note that changing your axes to the usual stuff. Eyes fine. As to the usual thiss crossed out. Where is fine. You just have to make sure your angle's right. Your calculations and so part B. You want to find attention on the cables. And so for this you course using Second lawyer was off forces in the Let's look at the X direction. Uh, for the ex director for direction, there's the equilibrium. Same for the what? For the wind direction. So that force is zero. And so what you have is the ex component of tension. Add it to the white component of two bags, component of gravity to be equal to zero. Okay, so ex competitive tension. It's just tea. So tea is acting that way, and you have a 31 degree angle. Your ex component would be this so t So you need a co sign Darkie Coast Starting one. Right? And then you have weight, which is acting this where? And you downwards. And you have angle of 25 degrees there. Uh, so so basically this. So basically, you have w acting this way. This is the direction you want Bret on along your x axis. So for that, you would need a sign there because, uh, because this is really what you want. Hey on. And it's going in the opposite direction. Notice from tension. So this would be a negative. W sign 25. That's zero. Okay. And said w the weight is travel the people's and she saw mass times. Gravitational acceleration mass is now 11 30 kilograms. Uh, she is, of course, is my 0.8 liters per second squared. So rate would be 11,000. Um, 11,074 news. Okay, so this means that t co signed 31. This is equal to 11,000 and 74 sign 25. And so T attention in the cable is just 5,460 news. Okay, cook, um, moving on to part scene you want now you want the normal force exerted by the ramp on the car. So this end in the free by diagram on DH. So again you resolve forces when second Lau and in the white direction it is also an equilibrium centre for since zero. This means that t sign 31 plus and these are the upward force is there? And is that no angle to the Y axis? So we're fine. He signed 31 plus n of miners, the force of the component of gravity acting directed downwards. And so this isn't quite w because it is an inclined ram. Uh, So this would be w co signed 25 that is equal to zero and again co sign because this time you're interested in here in the you're interested in the this direction, right? As opposed to the perpendicular direction. So now you want a co sign instead of the sign and so we have to We have w so n is just w coast 25 Bias a team sign 31. And so that's 11 074 Coast 25 minus 5,460. Sign 30 31. And this gives you normal forests of 7,220. That's it.

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