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Simon Fraser University

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00:56

Donald A.

I) How much tension must a rope withstand if it is used to accelerate a 1210-kg car horizontally along a frictionless surface at 1.20 m/s$^2$ ?

00:48

Averell H.

(I) What force is needed to accelerate a sled (mass = 55 kg) at 1.4 m/s$^2$ on horizontal frictionless ice?

04:39

Muhammed S.

(I) A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?

03:02

(II) Superman must stop a 120-km/h train in 150 m to keep it from hitting a stalled car on the tracks. If the train's mass is $3.6 \times 10^5$ kg how much force must he exert? Compare to the weight of the train (give as %). How much force does the train exert on Superman?

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welcome to our second unit in Dynamics, where we will discuss Theo idea of friction force frictional force. So friction is an idea that's already come up. You know, it's resisted force. It's when you're sliding something across the floor and it resists the motion of that. You have to push it harder than you might have thought you would, because of the friction between the floor and the object that you're pushing now, um, were we all recognize fiction in a scenario like that, we're in object is sliding. But what a lot of people don't realize is that there are two types of friction. There's actually more, but we're gonna discuss to Here they have static and kinetic friction. So static means that an object is not moving, meaning the two surfaces have relative velocity of zero. That means they're not sliding over each other. Meanwhile, kinetic friction just means that they are sliding, so there is a velocity between the two surfaces. So when the two objects they're not moving as one thing when the two objects are moving, it's another thing we're gonna model both with a very simple model. We're going to say that the force due to friction is proportional. This is this means is proportional to normal force, so forced affection is proportional to normal force. Okay, um and we're gonna go ahead and say, you know what? I'm gonna I'm gonna guess that is proportional by some constant that I'm going to call mute. So this is the Greek letter mu I'm using here, and it's used to represent what's called the coefficient of friction. You can go ahead and look up coefficients of friction online or in your textbook. There will certainly be a list in both meet, and it will give you the coefficient of friction not just for a surface, but between two surfaces. Because remember, it requires two surfaces to be able to observe friction. So you might have rubber on rubber or you might have metal on ice or anything else that you might be interested in. You could probably find an approximate coefficient of friction for that object. Now, would you? When you pull up the table, you're going to see something odd. You're gonna get to coefficients of friction one for static friction, where you'll have a Musa best and one for kinetic friction. Where you'll have, um, Yusef K. And you'll notice that always, always, always the static friction coefficient is going to be greater than the kinetic friction coefficient. That's why when you start pushing an object, you have to actually push harder to get it sliding. And then once it's sliding, it's easier. So usually you'll get you'll push, push, push and then it'll slip and continue moving forward if you keep on applying a force to it. Um, the way we model that mathematically is we say that FM UK is just simply equal to mu K times fn. Remember, normal force here could be the weight of the object. Or it could be the force at which it's being pushed against the surface. And then So we have kinetic friction. And then we also have static friction, which isn't an equation. It's actually an inequality, so it looks very much the same as kinetic friction. Aside from that, So instead of being equal to its either less than or equal to Mu s times fn, remember, Since Mu s is always greater than UK, it means that this will always be a larger force than this. Now what does this inequality mean? What it means is that you can apply a range of forces to an object and have it not move. Find something on the desk next to you or on the floor and try pushing it with a lot of different forces. So you just put your hand on it and start to push it. Not enough to make it move, but push it harder and harder and harder until it slips a little than back off a little. And you'll notice that you can apply Ah, whole bunch of different values of forces to this object and have it not go anywhere. It won't slip at all. This is because of the inequality FM. US is less than or equal to Mu s fn. Okay, Eso What we're saying here is that we have some value, and as long as we don't apply more than that force, nothing's going anywhere. So when we draw the free body diagram, it would look like this. We'd say I have f g. I have f n have a force f and I have f u s. And as long as it's FM us, it means the F minus. F M us is equal to zero because we have no acceleration because FM us is perfectly matching f and it doesn't matter if you change it. You could have f equals 10 Newtons and then change it to five Newtons or one Newton, an FM us will immediately respond to be the exact same value in the opposite direction. Likewise, if you were suddenly to jump around and stop this force and start pushing from the right side instead of the left hand side, then frictional force would switch directions to and it would oppose you again. Static friction is an opposing force, just like how kinetic friction is. It's just that static prediction friction prevents motion. So this could be a little hard Thio stick with conceptually and even mathematically. But we'll do examples of it. Don't worry. Kinetic friction is much easier. We say I have a box. I want to push it with five Newtons. It has a mass of 1 kg. What's the Net force that it experiences? Well, assuming we have, um, you equal to 0.1 UK and we draw a free body diagram, we're already assuming that the object is moving. We're not gonna worry about static friction at this moment. We push it forward with five Newtons. It's going to experience a force f M u K backwards. So we write out our Newton's second law five Newtons to the right minus F M u K to the left is equal to mass times acceleration. Well, in this case, FM UK, which is still equal to mu k times fn notice that FN here. When we write it in the Y direction, we're gonna have FN minus f G equals zero because it's not bouncing up and down in the Y direction. It means f n is equal to MGs. We have, um UK times m times G. So that's about 10 times one. So that's 10 Newtons times 100.1. That's one Newton so we can rewrite our equation. Five Newtons minus one Newton sequel to mass times acceleration masses one. Therefore, a is equal to four meters per second squared, so you need to equations. You need Newton's second law and you need the definition of kinetic friction and using these two equations you're able to solve for what's happening here. You can solve for FM UK and then you can solve for acceleration. So we'll continue to do problems here in the coming videos where we'll consider things like How hard do you have to push an object to get it moving? So So you have to push it with Force F and then once it starts moving, if you continue pushing with that force, how fast is accelerating? Or I could ask things like, Hey, you get an object moving and then it continues to move with a constant velocity. What's going on? Well, constant velocity just means remember that there is no Net force. It doesn't mean that there is zero force on it. For example, in the Y direction, there's two forces they just happen to always be balancing. Similarly, we say we're pushing it to the right with a force F, and it's sliding. So it's a kinetic friction force, but it's an acceleration is zero acceleration is zero. Then we have F minus. F M. U K equals zero because acceleration is zero, So M times a zero, which means that we have f is equal to FM UK. So we definitely want to make sure we're paying attention to whether the object is moving with a constant velocity or with some acceleration, please take a look at the coming example videos. There's a lot of little things to friction that students miss, and a lot of it has to do with drawing accurate, free body diagrams.

Work

Kinetic Energy

Potential Energy

Equilibrium and Elasticity

Energy Conservation

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