Question

A spring-loaded dart gun with spring constant k shoots a dart straight up. The spring has an initial compression x and is released from rest. The dart reaches a maximum height h. If we wanted the dart to go four times as high, how much should we compress the spring?

x

2x

4x

16x

Answer 1

Here no external force is applied to the system comprising of spring and dart.

So total energy of the system is conserved.

By applying the conservation of energy principle, we get that initial PE of the spring is converted to final PE of the dart.

So to increase the height four times, we need to compress the spring as twice before.