Question

Why does your foot hurt more when you stone than when you hit a football ?

Answer 1

Newton’s third law of motion is the basis of every action and reaction force. We must be clear about all the three laws by Newton in order to understand and solve the question. Every law has some impact upon each other so it is important to clarify all the three laws in order to understand the solution.

Complete answer:
According to Newton's third law of motion, every action has an equal and opposite reaction i.e., when a substance applies a force on another substance then the later substance also exerts a force equal in magnitude and opposite in direction upon the former substance.

Now according to this law, it is clear that both (stone and football) must apply a force on foot when kicked. According to Newton’s first law of motion, a body remains in its state of inertia (rest or motion) until and unless an external force is applied on it. The 1st law defines the state of inertia (rest) of stone and ball and says that both are applicable to equal amounts of force by foot.

Newton’s second law of motion states that force applicable on any substance is directly proportional to mass of substance and acceleration produced. Force applied defines the extent of change in inertia to be produced in substance.It proves that stone, due to its heavy weight, requires more force to generate change in inertia than football.

All the laws conclude that on kicking a stone, due to its heavy weight, it requires more force to change its inertia of rest and as more force is applied on it so it will generate more reaction force on foot. (As compared to football). As the reaction force is large, so will be the hurting of kicking a stone versus kicking a football.

Note: Impulse is quite related to force and inertia but is completely a varied term.Impulse is the time integral of force for the duration it is acted. It can be a starting sudden force that changes the state of inertia of the body.