A cannon fires, and the cannon itself jumps backward. Nothing hit the cannon. Why should firing a ball forward send the cannon backward?
The law of conservation of momentum covers more than collisions. A separation, where two objects at rest push apart, obeys exactly the same law.
Before the shot, the cannon and the ball sit at rest. Take them together as the system. The system's total momentum is zero.
The forces of the shot are internal: the ball and the cannon act on each other. Along the ground, the net external force on the system is roughly zero during the shot.
So the law applies: the total momentum stays constant. It was zero, so it stays zero.
After the shot, the ball carries momentum forward. For the total to stay zero, the cannon must carry momentum of equal size in the opposite direction.
That backward motion is called the recoil. Two objects pushed apart from rest carry equal and opposite momenta.
Equal momenta never means equal speeds. The ball's momentum sits in a small mass, so its velocity is large; the cannon's same-size momentum sits in a large mass, so its velocity is small.
A cannon at rest fires a ball. Just after the shot, how does the cannon's momentum compare with the ball's?
Two hockey players at rest push apart on smooth ice. Which statement explains why their momenta are equal in size and opposite in direction just after?
Two roller skaters stand at rest, then push apart. The lighter skater glides away with momentum 60 kg·m/s leftward. State the heavier skater's momentum just after.
Before the push, the two-skater system is at rest: the total momentum is zero.
The forces of the push are internal, and the net external force is roughly zero, so the total stays zero.
The lighter skater carries 60 kg·m/s leftward, so the heavier skater must carry 60 kg·m/s rightward for the total to stay zero.
The heavier skater's momentum is 60 kg·m/s rightward: equal in size, opposite in direction.
Katya says: the law of conservation of momentum applies when two objects push apart from rest, not only when objects collide. Is she correct?
A skateboarder stands at rest on her skateboard, which is much lighter than she is. She steps forward off it. What does the skateboard do?
Take the direction of the ball's motion as positive. A 500 kg cannon at rest fires a 5.0 kg ball. Just after the shot, the ball's momentum is +100 kg·m/s. Enter the cannon's momentum just after, in kg·m/s.
Two objects push apart from rest. Which statement is correct just after the push?