Newton's Second Law

Force, mass and acceleration

Newton's Second Law of motion can be described by this equation:

resultant force = mass × acceleration

F = m~a

This is when:

  • force (F) is measured in newtons (N)
  • mass (m) is measured in kilograms (kg)
  • acceleration (a) is measured in metres per second squared (m/s²)

The equation shows that the acceleration of an object is:

  • proportional to the resultant force on the object
  • inversely proportional to the mass of the object

In other words, the acceleration of an object increases if the resultant force on it increases, and decreases if the mass of the object increases.

Inertial mass - Higher

The ratio of force over acceleration is called inertial mass. Inertial mass is a measure of how difficult it is to change the velocity of an object.

Example

Calculate the force needed to accelerate a 22 kg cheetah at 15 m/s².

F = m~a

F = 22 \times 15

F = 330~N

Question

Calculate the force needed to accelerate a 15 kg gazelle at 10 m/s².

F = m~a

F = 15 \times 10

F = 150~N

Estimations

It is important to be able to estimate speeds, accelerations and forces involved in road vehicles. The symbol ~ is used to indicate that a value or answer is an approximate one. The table gives some examples.

VehicleMaximum legal speed on a single carriageway in m/sMass in kgAcceleration in m/s2
Family car~27~1,600~3
Lorry~22~36,000~0.4

Example

Estimate the force needed to accelerate a family car to its top speed on a single carriageway.

Using values of ~1,600 kg and ~3 m/s2, and F = m a:

1,600 × 3 = ~4,800 N

Question

Estimate the force needed to accelerate a lorry to its top speed on a single carriageway.

Using values of ~36,000 kg and ~0.4 m/s2, and F = m a:

Force (F) is ~14,400 N