Question

A catapult throws a stone of mass $0.10kg$ with a velocity of $\raisebox{1ex}{$30m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. If $25\%$ of the PE of the elastic band is wasted during transmission, find the magnitude of PE.

Answer 1

Step 1: Given data,

Mass = $0.10kg$

Velocity = $\raisebox{1ex}{$30m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Step 2: To find the kinetic energy of a stone:

Formula used:$Kineticenergy=\frac{1}{2}\times mass\times {\left(velocity\right)}^2$

$$\begin{gathered} E_K=\frac{1}{2}m{v}^2 \\ =\frac{1}{2}(0.10){\left(30\right)}^2 \end{gathered}$$

$=45J$

Step 3: Calculate the potential energy,

The kinetic energy of the stone = $25\%$ less than the potential energy of the catapult.

$\Rightarrow$Kinetic energy of a stone = $75\%$of the potential energy of a catapult

$45J=0.75\times PE$

$PE=\frac{45}{0.75}=$$60J$

Therefore, the magnitude of the potential energy is $60J$.