The spring constant for the spring in a special cannon is 1800 n/m. in cocking the cannon, the spring is compressed 0.55 m. what is the initial speed of a 7.0-kg cannonball at rest on the free end of the spring when it is released

The elastic potential energy of the spring when it is compressed is given by

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:


When the spring is released, all this energy is converted into kinetic energy of the cannonball, given by:

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, , and using m=7.0 kg we can find the speed of the cannonball with the previous equation:

Answer: fn = wcos50 = 38.89(9.81)(cos50) = 245.23 n

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