Only Net Force Equals ma for AP Physics B & C

Practice problems for these concepts can be found at: Newton's Second Law, Fnet = ma Practice Problems for AP Physics B & C

THIS IS REALLY IMPORTANT. Only F_net can be set equal to ma. You cannot set any old force equal to ma. For example, let's say that you have a block of mass m sitting on a table. The force of gravity, mg, acts down on the block. But that does not mean that you\ can say, "F = mg, so the acceleration of the block is g, or about 10 m/s²." Because we know that the block isn't falling! Instead, we know that the table exerts a normal force on the block that is equal in magnitude but opposite in direction to the force exerted by gravity. So the NET force acting on the block is 0. You can say "F_net = 0, so the block is not accelerating."

A Simple Example

We follow our four–step process. First, draw a proper free–body diagram.

Second, we break the Fpush vector into components that line up with the horizontal and vertical axes.

We can now move on to Step 3, writing equations for the net force in each direction:

Now we can plug in our known values into these equations and solve for the acceleration of the block. First, we solve for the right–left direction:

Next, we solve for the up–down direction. Notice that the block is in equilibrium in this direction—it is neither flying off the table nor being pushed through it—so we know that the net force in this direction must equal 0.

So the acceleration of the block is simply 2.2 m/s² to the right.

Practice problems for these concepts can be found at: Newton's Second Law, Fnet = ma Practice Problems for AP Physics