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$\bullet$$\bullet$ Some sliding rocks approach the base of a hill with a speedof 12 $\mathrm{m} / \mathrm{s}$ . The hill rises at $36^{\circ}$ above the horizontal and hascoefficients of kinetic and static friction of 0.45 and 0.65 .respectively, with these rocks. Start each part of your solutionto this problem with a free-body diagram. (a) Find the acceler-ation of the rocks as they slide up the hill. (b) Once a rockreaches its highest point, will it stay there or slide down thehill? If it stays there, show why. If it slides down, find its accel-cration oa the way down.

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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

University of Washington

University of Winnipeg

Lectures

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Okay, So here are the three body migrants will vote cases in part, uh, well, and been in both cases, you have jack downwards out of things. Normal force acting directly afterwards. But in part, you have velocities upwards emotions off the hill. So to oppose that fictional force will be directed down the hill. The part you have motion, you have motion down the hill. And so to oppose official sources. Okay, so in part way resolved force in the white direction, that's you. So end little farce, a vehicle to the vertical component of rate. So that will be edgy. Co sign six and then resolving in the ex direction you get, uh, that there isn't a force there. Uh, so you have that, Uh, that's a care which, like, Downwards Plus and she horizontal component out. Chief six, delete the call. Two em. Hi, Max. That's a super PACs. We'll just be absolute. Care is mix of care. Uh, confession, canary affection times and And so end is mg Coast 36 plus, uh, and she signed 36. Uh, you can take you can take. And so are you. And is it about you could take em out. Both sides get G turns. Music care Coast 36 us fine. Six. She ends that quite eight. Yusuke is great. 45 Official Kinetic friction. It's the last recall. Nine points use per second squared search. We assume downward direction. That's positive. She's mine. Just seconds squared down. So X is acting downwards. Uh, okay. And in part B, it's a similar situation. Uh, theory, Uh, the only major, the only difference really is force infection acting. Uh, the opposite direction s a maximum maximum static friction force, remember is just, uh, abusive ass official static friction turns and and and is still equal to energy co side 36. That hasn't changed at all. And so that will be 0.65 the coefficient of static friction times and she mg co side 36. And so that's this 0.5 to 6 mg. Hey, now and and let's leave it at that right now, never use all forces the extraction, and there is an attic salvation. And we get mg signed 36 again, but this time minus the friction force. So this will be absent. Asked that we just calculated that were equal to em time. Result of acceleration. And so the acceleration is just of MG side. 36 miners, our entire exploration and 77 36 minus 77 36 360.5 to 6 g on's drop out. She is 9.8 and some acceleration. It's 2.19 meters per second squared, so it does move. It does. It does move down, Hill. Uh, and, uh, this acceleration is moving is moving downhill at with a magnitude of 2.19 meters per second squared.

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