Newton’s Second Law

Unbalanced forces

When the forces acting on an object do not balance, the resultant force will cause the object to accelerate in the direction of the resultant force.

In other words, a resultant force on a body will cause it to change its velocity. This simply means that unbalanced forces will cause:

  • acceleration
  • deceleration
  • change in direction
curriculum-key-fact
A resultant force is the leftover or net force when all the forces acting on the object have been combined.

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

{\text{resultant force (N)}}={\text{mass (kg)}}\times{\text{acceleration (m/s}^{2}}{\text{)}}

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

You will have to be able to state this equation in the examination.

Question

A car weighs 1,000 kg. The resultant force is 5,000 N. Use the Fma triangle to find the acceleration of the car.

A formula triangle showing Force is equal to Mass multiplied by Acceleration.

Acceleration = resultant force ÷ mass

a = 5,000 N ÷ 1,000 kg = 5 m/s2

Resultant force and calculating acceleration

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.

To calculate the acceleration, you must find the resultant force so that you can divide it with the car's mass.

The resultant force = 4,000 N - 1,000 N = 3,000 N

\text{acceleration}=\frac{\text{resultant force}}{\text{mass}}

= 3,000 N ÷ 1,000 kg

= 3 m/s2

The first car accelerates because the car is moving in the same direction as the resultant force. Now look at the second car.

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).

Resultant force = -7,000 N

\text{acceleration}=\frac{\text{resultant force}}{\text{mass}}

= -7,000 N ÷ 1,000 kg

= -7 m/s2

The second car decelerates. It is moving in the opposite direction to the resultant force.

Acceleration and mass are inversely proportional. This means that if the mass of the vehicle doubles, the acceleration halves if the resultant force doesn’t change.

Resultant force and acceleration are directly proportional. If the resultant force doubles, the acceleration of the vehicle also doubles if the mass of the vehicle is the same.

Question

A car has a mass of 1,200 kg, and an engine that can deliver a force of 6,000 N. Find the acceleration of the car.

a = F ÷ m

= 6,000 N ÷ 1,200 kg

= 5 m/s2

Question

Find the force developed by a speed boat engine, if the boat has a mass of 300 kg and can accelerate at a rate of 1.5 m/s2.

F = m × a

= 300 kg × 1.5 m/s2

= 450 N

Question

In a theme park, one of the rides has a motor that can deliver a force of 3,600 N to an empty passenger car, causing it to accelerate at 4.5 m/s2.

Find the mass of the car.

m = F ÷ a

= 3,600 N ÷ 4.5 m/s2

= 800 kg