Question

Why can we neglect forces such as those holding a body together when we apply Newton’s second law of motion?

Short answer

Internal forces acting on a body are equal and opposite in direction, so their sum must be zero. Therefore, there can be no net force from the internal forces.

Step-by-step solution

Concept of Newton’s second law of motion

Newton’s second law of motion states that the acceleration of a system is directly proportional to the net external force acting on the system and is inversely proportional to the mass of the system. Mathematically,

$F_{net}=ma$

Herelocalid="1654165093803" ${}^{F_{net}}$is the net force,localid="1654165395003" ${}^m$is the mass, andlocalid="1654165421915" ${}^a$is the acceleration.

Explanation for neglecting the internal forces

According to Newton’s first law, the change in motion is due to the net external force. Internal forces are responsible for holding together a given body. The internal forces do not affect the motion of a body. The motion of a body is affected only by external forces.

Internal forces acting on a body are equal and opposite in direction, so their sum must be zero. Therefore, there can be no net force from the internal forces.