On the surface, Newton's Second Law of Motion seems like a simple little equation, but in
reality, it is one of the most powerful and useful equations in introductory physics.
F = m * a
Yep, that's it. Just those three little variables. Force equals mass times acceleration.
Notice, though, how there is no subscript after the F. The reason is that this equation is
designed to adapt to many different situations. To show you basically how this equation works,
we're going to do a quick sample problem. After that, I'm going to show you how to do a shortcut
using this formula.
A body accelerates at 10m/s2 when a 5N force is applied to it. What is the body's mass?
5N = m * 10m/s2
0.5kg = m
See, real easy. Now, do you remember how we used to figure out the force of gravity? Using
that formula FG = (g * m1 * m2)/r2, right? We know that the acceleration of objects near the
surface of the earth is -9.8m/s2, so if we know the mass of the object, we can use our new
formula to easily find the force of gravity on all objects near the surface of the earth. Just a
note, when using the earth's acceleration in this formula, there is no need to include the
negative sign. Let's do a quick example.
What is the force of gravity between the earth and a 50kg person standing on its surface?
FG = 50kg * 9.8m/s2
FG = 490N
Cool, huh? Because we were finding the force of gravity, I went ahead and made the force
variable FG. But really, it can be whatever you need it to be, as long as you have the correct
acceleration for it. Let's do lengthier problem now.
A 10kg block of wood is given an initial velocity of 15m/s. After traveling 20m, it comes to
a stop, what is the coefficient of kinetic friction between the block and the floor?
First, let's find the force of gravity, and begin drawing our force diagram.
FG = 10kg * 9.8m/s2
FG = 98N
The only equation in our arsenal with mK is a, so therefore we need to use the equation 2 * a * d = vf2 - vo2.
I will show these steps in calculations below.
2 * a * 20m = (0m/s)2 - (10m/s)2
40m * a = -100m2/s2
a = -2.5m/s2
FK = 10kg * -2.5m/s2
FK = -25N
25N = 
K * 98N
K = .255
See how helpful Newton's Second Law is. We even used it twice in that last problem. Overall,
F = m * a is a very useful formula.
Newton's Third Law is really more of a concept than a formula,
but it does deserve mentioning becuase it is still interesting.
