Question

A marshmallow gun uses a spring to launch marshmallows.The spring has a spring constant of 200 N/m.The marshmallow has a mass of 0.05 kg and when the marshmallow gun is fired straight up into the air,the marshmallow reaches a maximum height of 18 meters.What is the mechanical energy in the system?

Answer 1

8.8 J

Step-by-step explanation:

The mechanical energy of the marshmallow + gun system is conserved. At the beginning, all the energy is stored in the compressed spring; when the marshmallow is fired, this energy is converted into gravitational potential energy: so the mechanical energy of the system is equal to the gravitational potential energy of the marshmallow when it is at its highest point. Therefore, it is

`E=U=mgh`

where

m = 0.05 kg is the mass of the marshmallow

g = 9.8 m/s^2 is the acceleration due to gravity

h = 18 m is the maximum height

Substituting, we find

`U=(0.05 kg)(9.8 m/s^2)(18 m)=8.8 J`