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To unload a bound stack of plywood from a truck, the driver first tilts the bed of the truck and then accelerates from rest. Knowing that the coefficients of friction between the bottom sheet of plywood and the bed are $m_{s}=0.40$ and $m_{k}=0.30,$ determine $(a)$ the smallest acceleration of the truck which will cause the stack of plywood to slide, $(b)$ the acceleration of the truck which causes corner $A$ of the stack to reach the end of the bed in 0.9 s.

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18:11

Khoobchandra Agrawal

Physics 101 Mechanics

Chapter 12

Kinetics of Particles: Newton’s Second Law

Newton's Laws of Motion

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

Lectures

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.

09:37

Isaac Newton (4 January 1643 – 31 March 1727) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

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in a sense to unload balance that that's kind of a place loading. So bye coefficient. Bye. And aesthetic static for it is read six fact slide. The acceleration. Mhm. Corner staff. Yes. Okay. No. And the distance here from the plywood. Yeah. Two. So what we have here, You have the bed, we have two plywood Forrester friction for us to wait and now we have this acceleration. Why would with respect mr? Then we also have the acceleration of the truck and then the absolute acceleration. Five little kid o. Matic with. But ultimately, if I'm for to be static, This is zero. So this is this. So in the static situation, God, so force balance. See this would be direction per predict Yes, motion. Yes. And so we can see here acceleration. Thanks not you. Yeah. Now obviously we could have resolved those components and is to get the same result. So for statics we this and again, this is also now if we basically going all right subject, this is yes, relate everything. Emanate friction force, the normal forest. Um Right to wait gee we get this expression for the acceleration uh plywood and we know every and so that gives point squared and that would be also the excel the truck that way cause that this friction for us to out assume the maximum for us. So this would be the Mexico the truck things to slide. So if the truck accelerates any faster the supply, what's gonna start sliding down. Uh huh. Oh now they tell us that um we wanted to go this distance, tomatoes. Yeah, 2.97 tells us that the acceleration beast and the start from Acceleration must be 4.94 per second squared. And now we know that the acceleration palate equals acceleration the truck plus yeah, expect. And so we can all we have the directions for all so I can resolve them. Yes. And so this factor has no component. So when we do some forces in this direction, just this is which looks a lot like previous. Uh well now acceleration of the truck and now we have an prime voice saying just some other not. It also means that we don't know the friction force. So if we sum forces force balance in this direction to see that we get so for the new friction for us um You know We substitute for eight. Yeah we get this and then we get minus ah um times the acceleration of people. So again but that yes in this direction this um now the new friction forces the kinetic coefficient of friction. Yeah. Again after that it's just a bunch of allergy so we eliminate and the friction force. You wait as MG substitute everything. Mm. What acceleration of peace he so we can solve for a summer examination of the truck that's given by this expression here and plugging in our values That that is 4.17 m per. Yeah sure. So a couple of us to notice. Let's see. Let's say if our friction force, frictional force but a fishing pole fishing this will drop out on this out and then we'd have to know well the sign of Yeah um greater than or equal. Ah This one. Yes. Funny 20. That's if um if we have mm sign 0.8 and this. Ah what point? Uh Point. Hi thanks. Which means that actually this would have nothing. Which makes a lot of sense. Uh huh. No friction just wants to slip. And with that excel that way that makes it. Uh And I guess you can say they Yeah that's that's zero. This is one. This is So then we would see mhm kg plastic acceleration. Different word flat. We could still have this acceleration because of the slip back. But it would it would have greater. Let's see. What would that what Kinetic? A zero eat point? Why? Plus four point or I'm one. So we need an acceleration of 7.8. There's per second squared. Right? So that makes sense again. That accelerate everything kind of checks out with this form? Yeah. All right. Islamic.

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