a shell is fired from the cannon. the shell of mass 30kg is shot with an initial velocity of 30m/s. what is the momentum of the cannon just after the shell is shot ?
To find the momentum of the cannon just after the shell is shot, we need to consider the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant if no external forces act on it.
In this case, the system consists of the cannon and the shell. Before the shell is shot, both the cannon and the shell are at rest, so the initial momentum of the system is zero.
When the shell is fired, it exerts a force on the cannon, causing it to move in the opposite direction. According to Newton's third law of motion, the force exerted by the shell on the cannon is equal in magnitude and opposite in direction to the force exerted by the cannon on the shell.
The formula for momentum is:
Momentum = mass × velocity
Given:
Mass of the shell (m) = 30 kg
Initial velocity of the shell (v) = 30 m/s
Since momentum is a vector quantity, the momentum of the shell is calculated by:
Momentum of the shell = m × v = 30 kg × 30 m/s = 900 kg·m/s
According to the conservation of momentum, the momentum of the cannon (or the negative momentum of the shell) after the shell is shot will be equal in magnitude but opposite in direction to the momentum of the shell. Therefore, the momentum of the cannon just after the shell is shot is also 900 kg·m/s, but in the opposite direction.