Question

A spring gun has a spring constant of $80N/m$. The spring is compressed $12cm$ by a ball of mass $15gm$. How much is potential energy of the spring and what will be the velocity of the ball, if the trigger is pulled:

• A. $57.6J,87.6m/s$
• B. $67.6J,97.6m/s$
• C. $0.576J,76.8m/s$
• D. $noneofthese$

Answer 1

The correct option is C $0.576J,76.8m/s$

Spring energy $E=\frac{1}{2}k{x}^2=\frac{1}{2}80\times {0.12}^2=0.576J$

From conservation of energy

Maximum Spring energy = Maximum kinetic energy of ball

$E=\frac{1}{2}M{V}^2$

$V=\frac{2E}{M}=\frac{2\times 0.576}{0.015}=76.8m{s}^{-1}$

Velocity of ball is $76.8m{s}^{-1}$