Question

Old naval ships fired 11 kgkg cannon balls from a 240 kgkg 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 2.5×104 N/mN/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.

Part A What was the speed of the cannon ball if the spring compressed 52 cmcm when the cannon was fired? Express your answer to two significant figures and include the appropriate units.

Answer 1

here,

the mass of cannon balls, m1 = 11 kg

the mass of cannon , m2 = 240 kg

the spring constant , K = 2.5 * 10^4 N/m

A)

when the compression in the spring , x = 52 cm = 0.52 m

let the recoil velocity of cannon be v

using conservation of energy for the spring

0.5 * K * x^2 = 0.5 * m2 * v^2

2.5 * 10^4 * 0.52^2 = 240 * v^2

solving for v

v = 5.31 m/s

and

let the velocity of cannon ball be u

using conservation of momentum

m1 * u + m2 * v = 0

11 * u + 240 * 5.31 = 0

u = 115.8 m/s

the velocity of cannon ball is 115.8 m/s