Newton's Second Law

Newton’s Second Law follows from the results of the above experiments.

The relationship between the resultant force, the mass of the object and the object’s acceleration is:

Resultant force F = mass m x acceleration a

F = ma

F = resultant force in N

m = mass in kg

a = acceleration on m/s2

A formula triangle showing Force is equal to Mass multiplied by Acceleration.
{F} = {ma} {F} = {m}\times{a}
{m} =\frac{\text{F}}{\text{a}} {m} = {F} \div {a}
{a} = \frac{\text{F}}{\text{m}} {a} = {F} \div {m}

The newton N

The unit of force is the newton N.

One newton is the resultant force that gives a mass of 1 kg an acceleration of 1 m/s2 in the direction of the force.

1 N = 1 kg x 1 m/s2

Example

A car has a mass of 1000 kg and a resultant force of 5000 N acts on it.

Question

What is the acceleration of the car?

a = \frac{\text{F}}{\text{m}}

F = 5000 N

m = 1000 kg

a = \frac{\text{5000 N}}{\text{1000 kg}}

a = 5 m/s2

The acceleration of the car is 5 m/s2

curriculum-key-fact
When using the equation F = ma it is important to remember that F is the resultant force acting on the object.

In the example below two forces act on the car.

To calculate the acceleration, the resultant of the forces must first be found.

A car with 2 forces acting either side of it. On the left is Thrust of 4,000 newtons, on the right is Drag of 5,000 newtons.

a = \frac{\text{F}}{\text{m}}

The resultant force F = 4000 N - 1000 N

= 3000 N

F = 3000 N

m = 1000 kg

a = \frac{\text{3000 N}}{\text{1000 kg}}

a = 3 m/s2

The car accelerates because the car is moving in the same direction as the resultant force.

Now look at a second example. The forward force remains at 4000 N.

A car with 2 forces acting either side of it. The car is moving to the left. On the right there is a drag of 7,000 newtons (air resistance & braking).

a = \frac{\text{F}}{\text{m}}

The resultant force F = 4000 N - 7000 N = -3000 N

F = -3000 N

m = 1000 kg

a = \frac{\text{-3000 N}}{\text{1000 kg}}

a = -3 m/s2

The car now has an acceleration of -3 m/s2 or a deceleration of 3 m/s2.

It is moving in the opposite direction to the resultant force and slows down.