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

The height is 3.1m

Step-by-step explanation:

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

`E_e=(1)/(2)K*x^2\\E_e=(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=(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=(0.081J)/(9.8m/s^2*(2.7*10^(-3)kg))\\h=3.1m`