7. Friction, Inclines, Systems

Kinetic Friction

# Pushing Down on a Block with Friction

Patrick Ford

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All right, guys, let's check out this problem here. We've got a 20 kg box that's moving along the floor and we've got a downward force on it. So let me go ahead and sketch this out. We've got 20 kg boxes on the floor and we're pushing down on this box. I'm gonna call this F down and it's 30 Newton's. We know that the box is going to be keeping its velocity constants. V equals two. We want to figure out how hard do we have to push the box horizontally so that we can keep this box at constant speed. So basically, there's another force right here, which I'll just call regular F. And that's basically what we're trying to figure out. We have the coefficient of friction, So what we want to do first is draw a proper free body diagram. Let's go ahead and do that. So basically, our free body diagrams gonna look like this. We have a downwards mg and we look for any applied forces. We know there's two. We have one that acts downwards. That's f down. You know what that is? And then we have our horizontal force, which is our F that's we're trying to look for. Remember, there's two other forces. We have a normal force because it's on the floor. And then because these two surfaces are in contact and the rough we have some coefficient of friction, there's gonna be some friction. Now, if this box is moving to the right, then remember, Kinetic friction always has to oppose that motion. It always is in the opposite direction of velocity. So your F K points to the left like this. So that's your free body diagram now. So now we want to figure out this force here. So what we wanna do is write r f equals Emma. But first, I'm gonna pick a direction of positive. So I'm just usually going to choose up into the right to be positive. That's what we'll do here. So you're some of all forces in the X axis equals mass times acceleration. We're gonna start with the X axis because that's where that force pops up. All right, so we got our forces. When we expand our some forces, we got f. It's positive. And then we've got f k is to the left. So what about this acceleration here. What about the right side of this equation? Well, remember, we're trying to find is how hard we need to push this so that the box is moving at a constant 2 m per second if the velocity is constant and that means the acceleration is equal to zero. So, really, this is an equilibrium problem. So we've got zero here, so basically are applied force. Our mystery f has to balance out with the kinetic friction. So basically, when you move this to the other side, it's equal to F k. So that means your force is equal to mu k times the normal. Remember, that is the equation for kinetic friction. We have the UK it's 03 What about this normal force here? You might be tempted to write mg in place of the normal force. But I want to warn you against that because you're never going to assume that normal is equal to mg when you look at your free body diagram, what you have to do is you have to look at all the forces that are acting in the vertical axis and then basically use f equals m A to solve for that Normal. So we're gonna go over to the Y axis here and solve for normal. So this is the sum of all forces in the Y Axis equals M A. Y, similar to the x axis. And acceleration is going to be zero in the Y axis because that would mean basically, the block isn't gonna go flying into the air or go crashing into the ground. That doesn't make any sense. So now you expand our forces, we've got normal. Then you've got mg, and then you've got this f down. That's basically this additional force that's pushing the block down, and that's equal to zero. So when you saw for this, you're gonna get N is equal to when you move both of these over to the other side, you're gonna get 20 times 9.8 plus 30 if you go out and work this out in your calculator, going to 2 to 26. So this is the number that you plug back into this equation here, so basically your force is equal to 0. times to 26. So if you go ahead and work this out, what you're gonna get uh, you're gonna get 67.8, and that's your answer. So you get 67.8 Newtons, is how hard you need to push this thing.

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