Answer to Question #109456 in Mechanics | Relativity for Patricia

Question

Explain how it is possible for a small child and a large football player to have the same momentum. If the small child and the large football player were running side-by-side (same velocity) which would take more force to stop? Why?

Answer 1

What is momentum? It is mass times velocity. Therefore, at low velocity an adult footballer may have the same momentum as a not so heavy child running at a full speed:

$$p=m_fv_f=m_cv_c.$$

On the other hand, momentum can be expressed as

$$p=\frac{F}{t},\\ \space\\ t=\frac{F}{p}.$$

The force that makes the footballer and the child stop is the force of friction. Assume that the coefficient of kinetic friction is the same for both:

$$F=f=\mu mg.$$

Substitute this to the previous equation with force and expand the momentum:

$$t=\frac{\mu mg}{mv}=\frac{\mu g}{v}.$$

Therefore, for the same speed it may theoretically take the same time for them to stop.