The elastic potential energy of the spring when it is compressed is given by
[tex]U= \frac{1}{2}kx^2 [/tex]
where
k is the constant of the spring
x is the compression of the spring
Using k=1800 N/m and x=0.55 m, we find:
[tex]U= \frac{1}{2}(1800 N/m)(0.55 m)^2 = 272.3 J [/tex]
When the spring is released, all this energy is converted into kinetic energy of the cannonball, given by:
[tex]K= \frac{1}{2}mv^2 [/tex]
where
m is the mass of the cannonball
v is its speed
Since the potential energy of the spring is converted into kinetic energy of the ball, [tex]U=K[/tex], and using m=7.0 kg we can find the speed of the cannonball with the previous equation:
[tex]v= \sqrt{ \frac{2K}{m} } = \sqrt{ \frac{2 \cdot 272.3 J}{7.0 kg} }=8.8 m/s [/tex]
