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.

Inertia

The mass of an object is measured in kilograms (kg). The mass of an object is also a measure of its resistance to any change in its motion. This tendency of an object to continue in its current state (at rest or in uniform motion) is called inertia.

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