To really appreciate Newton’s Laws, it sometimes helps to see how they build on each other.
- The First Law describes what will happen if there is no force.
- The Second Law describes what will happen if there is a force.
The 2nd Law (The Law of Motion)
“When an external, unbalanced force acts on an object,
the object will accelerate in the same direction as the force. The acceleration varies directly as the force,
and inversely as the mass.”
“When an external, unbalanced force…”
We are still talking about these external forces, but now we’ve added in the idea of “unbalanced”.
- Unbalanced just means that there isn’t anyone (or anything) pushing against the force hard enough to cancel it out.
“…accelerates in the same direction as the force…”
Some people think this means that the object will move in the same direction as the force… not necessarily!
- The object might be moving to the right, while a force is pushing left.
- That means the object will slow down.
- It’s acceleration is in the direction of the force (to the left), but it is still moving to the right.
“The acceleration varies directly as the force…”
This just means that if the force increases, the acceleration will increase. If the force decreases, the acceleration decreases.
- This makes sense… push something harder and it will accelerate more! They depend directly on each other.
“…and inversely as the mass.”
This means that if the mass is bigger, the acceleration is less. If the mass is less, the acceleration is more.
- This makes sense also… if something has less mass, it is easier to make it move faster! They depend inversely on each other.
Mathematically this would be written as…
- The little swimming fish symbol ( α ) is the Greek letter “alpha” and means “varies as” in math.
- It does not mean they are equal to each other, but it does show they are related to each other in some way.
When you combine these two relations, you get one of the most basic and important formulas ever discovered in physics.
F = ma
F = force (Newtons)
m = mass (kg)
a = acceleration (m/s2)
The unit of force is called the Newton (equal to kg m/s2).
- It was named in honour of the outstanding work that Newton did in physics.
- By definition a one kilogram mass will be accelerated at 1 m/s2 if a 1 Newton force is applied to it.
Example 1: Determine the force acting on a 5.46kg object if it is accelerated at 17m/s2.
F = ma
= (5.46 kg)(17m/s2)
F = 93N
Example 2: Determine the acceleration of a 1000 kg car if a 2.5e3 N force acts on it?