The four example problems in this chapter were all solved using only F (^) net = ma . Problems you might
face in the real world—that is, on the AP test—will not always be so straightforward. Here’s an example:
imagine that this last example problem asked you to find the speed of the blocks after 2 seconds had
elapsed, assuming that the blocks were released from rest. That’s a kinematics problem, but to solve it,
you have to know the acceleration of the blocks. You would first have to use F (^) net = ma to find the
acceleration, and then you could use a kinematics equation to find the final speed. We suggest that you try
to solve this problem: it’s good practice.
Also, remember in Chapter 12 when we introduced the unit of force, the newton, and we said that 1 N
= 1 kg·m/s^2 ? Well, now you know why that conversion works: the units of force must be equal to the units
of mass multiplied by the units of acceleration.
Exam tip from an AP Physics veteran:
Newton’s second law works for all kinds of forces, not just tensions, friction, and such. Often what
looks like a complicated problem with electricity or magnetism is really just an F (^) net = ma problem, but
the forces might be electric or magnetic in nature.
—Jonas, high school senior
Newton’s Third Law
We’re sure you’ve been able to quote the third law since birth, or at least since 5th grade: “Forces come
in equal and opposite action-reaction pairs,” also known as “For every action there is an equal and
opposite reaction.” If I push down on the Earth, the Earth pushes up on me; a football player who makes a
tackle experiences the same force that he dishes out.
What’s so hard about that? Well, ask yourself one of the most important conceptual questions in first-
year physics: “If all forces cause reaction forces, then how can anything ever accelerate?” Pull a little lab
cart horizontally across the table ... you pull on the cart, the cart pulls on you, so don’t these forces cancel
out, prohibiting acceleration?
Well, obviously, things can move. The trick is, Newton’s third law force pairs must act on different
objects , and so can never cancel each other.
When writing F (^) net = ma , only consider the forces acting on the object in question. Do not include
forces exerted by the object.
Consider the lab cart. The only horizontal force that it experiences is the force of your pull. So, it
accelerates toward you. Now, you experience a force from the cart, but you also experience a whole
bunch of other forces that keep you in equilibrium; thus, you don’t go flying into the cart.