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$\bullet$ $\bullet$ A block with mass 0.50 $\mathrm{kg}$ is forced against a horizontalspring of negligible mass, compressing the spring a distance of$0.20 \mathrm{m},$ as shown in the accompanying figure. When released,the block moves on a horizontal tabletop for 1.00 $\mathrm{m}$ before com-ing to rest. The spring constant $k$ is 100 $\mathrm{N} / \mathrm{m} .$ What is the coeffi-cient of kinetic friction $\mu_{\mathrm{k}}$ between the block and the tabletop?

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0.41

Physics 101 Mechanics

Chapter 7

Work and Energ

Physics Basics

Applying Newton's Laws

Kinetic Energy

Potential Energy

Energy Conservation

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Winnipeg

Lectures

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

03:34

A block with mass 0.50 kg …

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06:04

A block with mass 0.50 $\m…

A block with mass m = 0.50…

02:57

02:53

A block with mass $0.50 \…

02:02

Block Against Horizontal S…

02:15

You push a $2.0 \mathrm{~k…

04:49

A 1.80-kg block slides on …

06:33

Note: Neglect the mass of …

02:00

You push a 2.0 $\mathrm{kg…

05:42

When a 3.0-kg block is pus…

02:40

A light horizontal spring …

in this problem. We see there's a spring that has been compressed and a box is attached to the spring whenever the boxes released thus or yeah, whenever the boxes released the spring D compresses and pushes the box towards the right side. So since the surfaces friction surface has friction, that's why the box stops at a certain point. Ah, because the friction is being acted on the box on the opposite direction to the displacement. So if we called this point as 0.0.1, where the spring has been attached to the box and call, this point is point to where the box finally stops. We can say that at this point the box had initial velocity of zero. Um, it's going to be one because we're wanting that as one, and we tow or the final velocity will be here as well, because due to friction, the box has stopped. Now, before you use the question 17.16 from the textbook, we can see the following question. Ah, let me explain what this equation means. So K one our king karma is corresponding to the kinetic energy of the system, or, for example, ifyou're concerning the box, then this is the kind of the energy of the box, and the one here is denoting that it's in 0.1. Then you want is the potential energy at 0.1 and w other is some other form of energy. So in our case, it will be the friction and ah ah, energy due to the friction for So let's call it F s, which is acting this way. That's why the boxes stopping it here because it's kind of in against the direction of motion of the box and that point, too. We have the frantic energy and the potential energy, but we don't have this other form of energy because the box is stationary here. So let's try to evaluate each town one by one. So when the system is a 0.1, we see that the system is at rest. That means there is no candidate energy, since the very one term is here is zero, and we know that kind of thing. Energies have in peace grade, so if easier than we can get rid of our candidate energy term, so let's make that zero. Similarly, Kato will be here as well because we see that Vito is zero here. So let's make that zero as well. For the potential energy. We see that the spring has been compressed, so there would be potential. It is you do to that compression and we can write that as half. Okay, X one squared. Now we should not be confused with this K on DH this K, this is big hair which is denoting the kind of energy. And there's a small cave which is denoting the spring constant. So at this point, we'll have the potential energy and this other form of energy. Let me discuss living. Come back to that in a moment. But let's talk about the you do first. So you two is the and pretension. And at this point, we can see that since this is stationary. And if we fix this as our origin, Yes. So, like, if this is this is our origin, then in the white direction of motion, there is no motion. That means we don't have to use gravitational potential energy here, since the height is not changing. And then there's no other form of off energy that's present here so we can get it off this YouTube harm here. So now let's come back to this w other time. So this is just the word than due to some force so we can write, worked, and due to some force as, um w f in our case because this is the work of the two frictional force. And we can write that as f k call sign fi times s. Now, if you have done the previous problems, we I know that, um, Wharton is nothing but force times the displacement Dying's co signed five. Where Fei is the angle between the force and the displacement on DA again essence the displacement and forces thie in darkest forces. F k. So we What? What do we see about the angle Fei? Here we see that the displacement is on the right. Although the friction forces acting on the left that means the angle between the direction of the displacement and that the frictional force will be 1 80 degrees So we can set that as our fight. So let me right w if one more time we'll have f s. Oh, are we have f k? It is a fictional force. Then we have co sign five times s. And as we say, that fire is 1 80 degrees. Also. What? What can you say about the frictional force? So we know that frictional forces mieux que times the normal force and anarchist normal force will be m times g. Hey, so let's call it in. That means new K times and will be the frictional force and let substitute and by writing mg. So finally our wk becomes, um yeah, okay, mg Then let's call the displacement s. And for cause I in 1 80 we have caused 1 80 Please, We know that co sign one. It is negative one So we can write that as I'm Yuki m g s Right. So let's combine all the questions together so we know that this is no negative. This one is no negative But then the other times are all zero. So we'll have you won plus w other are in our cases affection. No, we're going to do frictional force will be zero So you want is half k X one squared Plus we mentioned w f s and negative new K MDs So it's negative Mut and d s. It is equal to zero. And from here, if you dare aerosol form Yuki, we'll have nuclear. It is equal to half off Key X one squared, divided by sometimes ci times s So if we plug in the numbers now will have half. Then K is 100 newton per meter. Yeah, excellent is 0.2 meters and then there's a square term and is 0.5 kg g is 9.8 meters per second. Squared and s is the displacement of these 1.0 meter using all the terms of the numbers. Together we get new K as zero point for one now is that there is no uniformity and we can see clearly. If we do, the calculation on the units will see that all the units get cancelled and we have Ah, we have any unit this quantity over here. Thank you.

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