Question

Old naval ships fired 14 kg cannon balls from a 250 kg cannon. It was very important to stop the recoil of the cannon, since otherwise the heavy cannon would go careening across the deck of the ship. In one design, a large spring with spring constant 2.0×10^4 N/m was placed behind the cannon. The other end of the spring braced against a post that was firmly anchored to the ship's frame.
What was the speed (in m/s) of the cannon ball if the spring compressed 56 cm when the cannon was fired?

Answer 1

Answer:

Speed of canon ball = V = 89.443 m/s

Explanation:

the spring potential energy will be converted into kinectic energy

M= mass of cannon

m= mass of cannon balls

k= 2.0*10^4 N/m

compression x= 0.56 m

0.5kx^2 = 0.5Mv^2

2 x 10^4 x 0.56^2 = 250 x v^2

Speed of canon = v = 5.008 m/s

Now,

we have, by momentum consevation

m x 0 + M x 0 = mV - Mv

0 = 14 x V - 250 x 5.008

Speed of canon ball = V = 89.443 m/s