Question

You are a pirate working for dread pirate roberts. you are in charge of a cannon that exerts a force 20000 n on a cannon ball while the ball is in the barrel of the cannon. the length of the cannon barrel is 2.41 m and the cannon is aimed at a 35⦠angle from the ground. the acceleration of gravity is 9.8 m/s 2 . if dread pirate roberts tells you he wants the ball to leave the cannon with speed v0 = 83 m/s, what mass cannon ball must you use? answer in units of kg.

Answer 1

Refer to the diagram shown below.

F = 2000 N, the force exerted on the cannonball
L = 2.41 m, the length of the barrel
V₀ = 83 m/s, the launch velocity
θ = 35°, the launch angle

Let m =  the mass of the cannonball.
Let a  =  the acceleration of the ball when fired.

The net force acting on the ball is
F - mg sinθ = 2000 - 9.8*m*sin(35°) =  2000 - 5.621*m N

Then, from Newton's Law of motion,
F = ma
2000 - 5.621*m = m*a             (1)

The launch velocity is V₀ = 8.3 m/s, therefore
V₀² = 2*a*L
(83 m/s)² = 2*(a m/s²)*(2.41 m)
6889 = 4.82*a
a = 6889/4.82 = 1429.25 m/s²      (2)

Insert (2) into (1)
2000 - 5.621*m = 1429.25*m
2000 = 1434.871*m
m = 1.394 kg

Answer: 1.394 kg