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Anderson Video - Book Gripping

Professor Anderson
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>> Hello class. Professor Anderson here. Let's take a look at a homework problem that deals with static friction and the idea is this. If you hold a book between your fingers, you grip that book, you can hold it vertically by applying a force to the book. If there is no friction, of course, between your fingers and the book, if your fingers are greasy the book will slip right out. So let's see if we can calculate how much weight you can hold, what the biggest mass is you can hold. And let's tell you a few givens. Okay. So here's the free body diagram. You have a pinch force n from each side that has a maximum of about, you know, 5 Newtons or so. Now if you are pinching it from the sides, you are applying a static frictional force that is vertical. And both sides of your grip are applying that force and so you have two f sub s going up. You are, of course, trying to fight against gravity going down. Okay. Let's also give a number for the static friction coefficient and let's say that's about 0.8. Okay. So the question is what is the maximum mass that you can hold by gripping the book in this manner? All right. So sum of the forces is equal to the mass times the acceleration. We've got sum of the forces in the x direction. That's not very interesting. That's just n from one side of the book minus n from the other side of the book. That is, of course, equal to zero. But what about the forces in the y direction? We have two of these frictional forces going up. We have mg going down. And if we are in equilibrium there is no acceleration. That thing is just equal to zero. All right. So now we can solve this last equation for m. m is equal to 2 f sub s over g. And we know what the maximum frictional force can be. The maximum static frictional force is mu s times the normal force n. Okay. That should make sense. The harder you grip it, the bigger n is, the bigger the mass is that you can hold. Okay. So now let's run some numbers and see what we get. We've got m equals 2 times mu s. We said that was 0.8. n we said was 5 newtons. And g is, of course, 9.8. We've got si units everywhere so we should end up in kilograms. And if we run those numbers, you should get 0.82 kilograms. Okay. Try it with your numbers. Hopefully it works out. And hopefully that's clear. If not, come see me in my office. Cheers.