Question

A $1kg$ mass falls from a height of $10m$ into a sand box. What is the speed of the mass just before hitting the sand box? If it travels a distance of $2cm$ into the sand before coming to rest, what is the average retarding force?

• A. $12m/s$ and $3600N$
• B. $14m/s$ and $4900N$
• C. $16m/s$ and $6400N$
• D. $18m/s$ and $8100N$

Answer 1

Answer: (B)

$14m/s$ and $4900N$

Here, we can equate the kinetic energy and potential energy when the mass travels a distance of 2 cm into the sand before coming to rest.

Since $\frac{1}{2}m{v}^2=mgh$

or, $v=\sqrt{2gh}$,

putting the values, we get:

$v=\sqrt{2\times 9.8\times 10}=14m/s$

Also, $Force\times displacement\left(d\right)=\frac{1}{2}m{v}^2$

So, $F=\frac{m{v}^2}{2\times d}$$=\frac{1\times 96}{2\times 2\times {10}^{-2}}$$=4900N$