Momentum Conservation

During Collisions In our force detector experiment we used a rubber band to slow down the collision so that we could do a more accurate analysis of the impulse. Even so the impulsive force acted for only a very short time. The most important point of the experiment is that, no matter how short the time is, the impulse, the time integral of is equal to the total change in momentum. If we had let the metal end of the cart strike the force detector, the collision would have taken much less time, but the force would have been much greater. The integral of the larger force over the shorter time would still equal the change in the momentum of the cart.
Suppose that, instead of an air cart colliding with a force detector, we had two air carts colliding with each other. During the collision they would by Newton’s third law, exert equal and opposite forces on each other. Thus they would exert upon each other equal and opposite impulses ∫dt . As a result, the momentum gained by one cart would precisely be equal to the momentum lost by the other. The net result is conservation of momentum during the collision.
Now consider a slightly more complex situation. Suppose I throw a red billiard ball up in the air, and you throw a blue billiard ball, and the two balls collide before landing.
During this collision, more forces are involved. There is the force of the red billiard ball on the blue one, the force of the blue billiard ball on the red one, and there are the gravitational forces acting on both. To study the change in the momenta of the balls, it appears that we must now account for all four forces at once.
However there is something special about the impulsive forces found in collisions. These forces are usually very large but act for a very short time. During this short time the collision forces are usually much larger than external forces like gravity. So much larger, in fact, that we can usually neglect external forces during a collision.
Since the collision forces conserve linear momentum, we get the result that linear momentum is conserved during a collision even if external forces are present. The only exception would be if the collision is so slow that the external forces have time to act and change the system’s momentum during the collision. This is usually not the case.

مواضيع ذات صلة

The Doppler effect

Finding the “apparent” motion

Series and parallel impedances

Analogs in physics

Oscillations in linear systems

Damped oscillations

The energy of an oscillator

The forced oscillator with damping

Complex numbers and harmonic motion

Forced oscillations

Initial conditions for Harmonic motion and circular motion

Harmonic motion and circular motion