Force = mass x acceleration
In SI units, the Newton's second law is written as
As a formula, it looks like this
where F is the force on a body, m the mass of the body, u its initial velocity, v the final velocity, and t the time take for this change in velocity to take place. Thus mu is the initial momentum, mv the final momentum, and the difference gives us the change. The ratio of this change to the time taken is then the rate of change.
In the above formula, m is a common factor in the bracket. It can be factored out like this:
In this form, we see that (v - u)/t is the change in velocity over time. This is just the acceleration a. Therefore, the formula can also be written in the popular form
This form allows us to make use of what we already know about acceleration, and deduce a few interesting effects that a force has on motion of a body.
First, the equation tells us that not only are the magnitudes of F and ma equal, but that the directions are also the same. That is, the direction of acceleration of the body is the same as the direction of the force acting on it.
We emphasise the phrase "direction of acceleration." Recall that this does not mean direction of velocity, and can often be different. If a body moves faster and faster to the right, then acceleration and velocity are in the same direction. If it slows down as it moves to the right, then direction of velocity is to the right, but direction of acceleration is to the left.
With this understanding, what can we deduce about the force if the body moving to the right is slowing down? Since acceleration is to the left, then according to F = ma, the force is also to the left. This is reasonable - the body slows down because the force is acting in the opposite direction to its velocity.
What if the body slows down to a stop and the force continues to act? Then the body would start accelerating to the left. This happens if I toss a stone upwards. The force of gravity slows down the stone. The stone stops for an instant when it reaches the highest point. The it falls the gravity continues to act.
Exercise. I push a book of mass 0.2 kg along a smooth table with a force of 0.5 N. Find the acceleration.
Solution. Rearrange F = ma to make a the subject: a = F/m. Then the answer is a = 0.5 / 0.2 = 2.5 m s-2.
Exercise. A book of mass 0.2 kg slides along a table at a velocity of 0.3 m/s. It slows down and stops in 4 s. Find the frictional force.
Solution. To use F = ma, we first find the acceleration. This is given by a = (v - u)/t = (0 - 0.3)/4 = -0.75 m s-2. So force F = ma = 0.2 x (-0.75) = -0.15 N. So the frictional force is 0.15 N. The minus sign means that the force acts in the opposite direction to the original direction of motion of the book. (By taking u as 0.3 m/s above, we have unconsciously taken the original direction of motion as the positive direction. We really should have decided on which direction is positive first, before using the equations.)
Copyright 2011 by Kai Hock. All rights reserved.
Last updated: 6 March 2011