All external forces on a body cancel out. Which statement must be correct?

Question 13

All external forces on a body cancel out.

Which statement must be correct?

A The body does not move.

B The momentum of the body remains unchanged.

C The speed of the body remains unchanged.

D The total energy (kinetic and potential) of the body remains unchanged.

Reference: Past Exam Paper – June 2013 Paper 12 Q13

Solution:

Answer: B.

All external forces on a body cancel out.

This means that the resultant force on the body is zero.

Resultant force = 0

ma = 0

The resultant force being zero means that the acceleration is also zero.

Acceleration is the rate of change of velocity. So, an acceleration of zero means that the velocity is not changing.

Consider choice A: The body does not move.

A body which is not moving means that its velocity is zero. Acceleration and velocity are two different quantities. No acceleration does not necessarily means that the velocity is zero. It only means that the velocity is not changing. The body may be moving at constant velocity; its acceleration would still be zero.

Consider choice B: The momentum of the body remains unchanged. [Correct]

Momentum p = mv

Since acceleration is zero, the velocity is not changing. So, the momentum is also unchanged.

Consider choice C: The speed of the body remains unchanged.

Speed is only the magnitude while velocity consist of a magnitude (speed) and a direction. When the acceleration is zero, it means that both the speed (magnitude) and the direction are not changing. The speed of a body may be constant but its direction is changing (for example, in circular motion). Then, the acceleration is not zero. So, the speed being unchanged does not necessarily means that the body is not acceleration as we also need to consider the direction.

This is why defining acceleration as ‘rate of change of speed’ is an incorrect definition.

Choice D: The total energy (kinetic and potential) of the body remains unchanged.

Force and energy are two different quantities. So, the resultant force being zero does not equal to the energy being unchanged.