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# Friction for AP Physics B & C

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Practice problems for these concepts can be found at:

Free-Body Diagrams and Equilibrium Practice Problems for AP Physics B & C

Friction is only found when there is contact between two surfaces.

For example, let's say you slide a book at a constant speed across a table. The book is in contact with the table, and, assuming your table isn't frictionless, the table will exert a friction force on the book opposite its direction of motion. Figure 10.3 shows a free-body diagram of that situation.

We know that because the book represented in Figure 10.3 is not being shoved through the table or flying off it, FN must equal the book's weight. And because the book moves at constant velocity, the force you exert by pushing the book, Fpush, equals the force of friction, Ff. Remember, being in equilibrium does not necessarily mean that the book is at rest. It could be moving at a constant velocity.

How do we find the magnitude of Ff ?

Mu (μ) is the coefficient of friction. This is a dimensionless number (that is, it doesn't have any units) that describes how big the force of friction is between two objects. It is found experimentally because it differs for every combination of materials (for example, if a wood block slides on a glass surface), but it will usually be given in AP problems that involve friction.

And if μ isn't given, it is easy enough to solve for—just rearrange the equation for μ algebraically:

Remember, when solving for Ff , do not assume that FN equals the weight of the object in question. Here's a problem where this reminder comes in handy:

The free-body diagram looks like this:

Now, in the vertical direction, there are three forces acting: FN acts up; weight and the vertical component of P act down.

Notice that when we set up the equilibrium equation in the vertical direction, FN – (mg + Py) = 0, we find that FN is greater than mg.

Let's finish solving this problem together. We've already drawn the vertical forces acting on the buffer, so we just need to add the horizontal forces to get a complete free-body diagram with the forces broken up into their components (Steps 1 and 2):

Step 3 calls for us to write equations for the vertical and horizontal directions. We already found the equilibrium equation for the vertical forces,

FN – (mg + Py) = 0,

and it's easy enough to find the equation for the horizontal forces,

FfPx = 0.

To solve this system of equations (Step 4), we can reduce the number of variables with a few substitutions. For example, we can rewrite the equation for the horizontal forces as

μ · FNP · cos 37° = 0.

Furthermore, we can use the vertical equation to substitute for FN,

FN = mg + P · sin 37°.

Plugging this expression for FN into the rewritten equation for the horizontal forces, and then replacing the variables m, g, and μ with their numerical values, we can solve for P. The answer is P = 93 N.

### Static and Kinetic Friction

You may have learned that the coefficient of friction takes two forms: static and kinetic friction. Use the coefficient of static friction if something is stationary, and the coefficient of kinetic friction if the object is moving. The equation for the force of friction is essentially the same in either case: Ff = μFN.

The only strange part about static friction is that the coefficient of static friction is a maximum value. Think about this for a moment … if a book just sits on a table, it doesn't need any friction to stay in place. But that book won't slide if you apply a very small horizontal pushing force to it, so static friction can act on the book. To find the maximum coefficient of static friction, find out how much horizontal pushing force will just barely cause the book to move; then use Ff = μFN.

Practice problems for these concepts can be found at:

Free-Body Diagrams and Equilibrium Practice Problems for AP Physics

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