Conservation of momentum has been a rule you check against data, and a law you state with its condition. A rule that reliable has a reason. The reason is a law you met earlier in this course: Newton's third law.
Follow one collision closely, with the impulse-momentum theorem in hand, and the conservation law falls out.
Two carts collide on a track. While they touch, cart A exerts a force on cart B, and cart B exerts a force back on cart A.
Newton's third law sizes the pair: the two forces are equal in size and opposite in direction.
Now the step that seems too small to say: the two forces act for the same time. The contact starts for both carts at the same instant and ends for both at the same instant.
Impulse is force times time. Equal forces, opposite directions, same time: the two impulses are equal in size and opposite in direction.
The impulse-momentum theorem turns each impulse into that cart's momentum change. So the two momentum changes are equal in size and opposite in direction.
Add the two changes and they cancel. Whatever momentum cart A gains, cart B loses. The system's total cannot move.
Take eastward as positive. In a collision between two gliders, glider 1's momentum changes by −2.4 kg·m/s. State glider 2's momentum change.
The gliders exert equal and opposite forces on each other for the same contact time.
So the impulses, and therefore the momentum changes, are equal in size and opposite in direction.
Glider 1's change is −2.4 kg·m/s, so glider 2's change is +2.4 kg·m/s.
Glider 2's momentum changes by +2.4 kg·m/s.
Two carts collide. The contact between them lasts 0.2 s for the lighter cart. How long does it last for the heavier cart?
In the same collision, the two forces are equal in size, opposite in direction, and act for the same time. How do the two impulses compare?
Isla says: in a collision the two momentum changes are equal in size and opposite in direction, so they cancel in the system's total, and that is why the total momentum stays constant. Is she correct?
Two shopping carts collide in an aisle. Why does the total momentum of the two-cart system stay the same through the collision?
Take rightward as positive. In a collision between a bowling ball and a pin, the ball's momentum change is −3.0 kg·m/s. Enter the pin's momentum change in kg·m/s.
A heavy truck and a light car collide head-on. Which statement about the sizes of their two momentum changes during the collision is correct?