A revolutionary war cannon, with a mass of
2170 kg, fires a 18.1 kg ball horizontally. The
cannonball has a speed of 146 m/s after it has
left the barrel. The cannon carriage is on a
flat platform and is free to roll horizontally.
What is the speed of the cannon immedi-
ately after it was fired?
Answer in units of m/s.
To find the speed of the cannon immediately after it was fired, we can start by applying the principle of conservation of momentum.
The momentum before the cannonball was fired is equal to the momentum of the cannonball and the cannon together. The momentum is given by the formula:
momentum = mass × velocity
Let's denote the mass of the cannon as Mc and the mass of the cannonball as Mb. The initial velocity of the cannonball is Vb, and we need to find the initial velocity of the cannon, Vc.
Using conservation of momentum:
(initial momentum of cannon + initial momentum of cannonball) = (final momentum of cannon + final momentum of cannonball)
Mc × Vc + Mb × 0 = Mc × Vc + Mb × Vb
Since the cannon is at rest before firing, the initial velocity of the cannon is zero (Vc = 0). We can simplify the equation to:
0 + 0 = 0 + Mb × Vb
Mb × Vb = 0
Therefore, the initial velocity of the cannon (Vc) is zero. This means that immediately after firing, the cannon is at rest.
So the speed of the cannon immediately after it was fired is 0 m/s.