Question

A dart is loaded into a spring-loaded toy dart gun by compressing the spring by a distance of $d$. For the next loading, the spring is compressed by a distance $2d$. How much faster does the second dart leave the gun compared to first?

• A. Four times
• B. Two times
• C. Half times
• D. One-fourth times

Answer 1

The correct option is B Two times

The energy stored in the dart due to the compression of spring gets converted into kinetic energy. If $m$ is the mass of the dart, then$\frac{1}{2}k{d}^2=\frac{1}{2}m{v}_o^2\left(where{v}_{o}isthevelocityinfirstcaseandkisspringcons\tan t\right)\frac{1}{2}k{\left(2d\right)}^2=\frac{1}{2}m{v}^2\left(wherevisthevelocityinsecondcase\right)\therefore \frac{1}{4}=\frac{v_o^2}{v^2}\Rightarrow v=2v_o$