Question

A moving body can be stopped by a force F in time t. How much force will be needed to stop the body in half the time when its momentum is doubled?

Answer 1

Dear Student,
Initial momentum = mu
Final momentum = mv = 0
Applied force = F
$$\begin{gathered} F=\frac{mv-mu}{t} \\ F=\frac{-mu}{t} \end{gathered}$$
Now the initial momentum is doubled then it takes t/2 time to stop the body.
New force = F'
$$\begin{gathered} F^{\text{'}}=\frac{0-2mu}{t/2} \\ F\text{'}=\frac{-4mu}{t} \\ F\text{'}=4F \end{gathered}$$
The required force to stop the body will become 4 times.
Regards