Question

A child’s toy that is made to shoot ping pong balls consists of a tube, a spring (k = 18 N/m) and a catch for the spring that can be released to shoot the balls. When a ball is loaded into the tube, it compresses the spring 9.5 cm. If you shoot a ping pong ball straight up out of this toy, how high will it go?

Answer 1

Answer:

The height is 3.1m

Explanation:

Here we have a conservation of energy problem, we have a conversion form eslastic potencial  energy to gravitational potencial energy, so:

$E_e=\frac{1}{2}K*x^2\\E_e=\frac{1}{2}18N/m*(9.5*10^{-2}m)^2\\E_e=0.081J$

then we have only gravitational potencial energy when the ball is at its maximun height.

$E_g=m*g*h$

because all the energy was transformed Eg=Ee

$h=\frac{0.081J}{9.8m/s^2*m}$

searching the web, the mass of a ping pong ball is 2.7 gr in average. so:

$h=\frac{0.081J}{9.8m/s^2*(2.7*10^{-3}kg)}\\h=3.1m$