A box of bananas weighing 40.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.20. (a) If no horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on it?

Video transcript

Hey, everyone in this problem, we have a 36 Newton pile of books resting on a horizontal table in a library. OK. The coefficients of static and kinetic friction between the box and the table are 0.36 and 0.22 respectively. OK. We're asked to determine the magnitude of the friction force on the pile when the pile is at rest. And horizontal force of magnitude F equals zero newtons is applied to the pile. OK? All right. So let's just draw this out. So we have a table here and that's not very horizontal. Let's try again. We have this horizontal table and we have a stack of books on top, right? And they're gonna be at rest. So converting this to a free body diagram. OK. This dot in the middle is gonna represent our books. We know that we have the normal force N acting upwards, OK. Perpendicular to the surface, we have the weight W acting downwards. OK? We have a force F that is applied to the pile, but we're gonna say that that force is applied to the right. OK. You could assume that it's applied to the left. Um, the answer will work out the same. Um, you'll just kind of switch signs throughout the problem. Ok. And we have um, friction between the box and the table or the books and the table. Ok. And so the friction is going to oppose the applied force. So it's gonna be acting to the left and that's gonna be our friction force. F. All right, we'll take up into the right to be positive. And this is our coordinate system. And we're asked to find the force of friction, the magnitude of the force of friction F. OK. And we see that F is acting in the X direction. So let's start with the sum of the forces in the X direction. OK. According to Newton's second law, recall that the sum of the forces in the X direction, it is going to be close to the mass times the acceleration in the X direction. And we're told that this pile is at rest. OK? At rest means that the acceleration is zero. And so the sum of the forces is going to be zero. Now, what is the sum of the forces in the X direction? We have this applied force F and then we have the force of friction little F acting in the opposite direction. So we have big F minus little F is equal to zero. And so a force of friction, little F is going to be equal to our applied force. F which we're told in the problem is zero newtons. Ok? And so when we're looking at our answer choices, we see that the magnitude of the friction force is going to be a zero newtons. That's it for this one. Thanks everyone for watching. See you in the next video.