Question

A vertical spring gun is used to launch balls into the air. If the spring is compressed by 4.9 cm, the ball of mass 5.5 g is launched to a maximum height 50.2 cm. How much should the spring be compressed to send the ball twice as high?

Answer 1

We know, by conservation of energy :

$\dfrac{kx^2}{2}=mgh$

Therefore,

$\dfrac{x_1^2}{x_2^2}=\dfrac{h_1}{h_2}$

Putting given values, we get :

$\dfrac{x_1^2}{x_2^2}=\dfrac{h_1}{h_2}\\\\\dfrac{4.9^2}{x_2^2}=\dfrac{50.2}{2\times 50.2}\\\\x_2^2=2\times 4.9^2\\\\x_2 = 4.9\times \sqrt{2}\\\\x_2=6.93\ cm$

Therefore, the spring be compressed to 6.93 cm to send the ball twice as high.

Hence, this is the required solution.