0.18 Phy1160: force and motion -- momentum, impulse, and conservation  (Page 8/14)

The can of rocks probably wouldn't go flying across the room, but might simply turn over, spilling the rocks on the floor.

The negative acceleration experienced by your foot might result in some broken toes.

Once again, the forces would be equal in magnitude and opposite in direction, but the acceleration of each object would be inversely proportional to the massof the object.

Equal and opposite forces

When you kick the can, your foot would exert a force on the can in the direction of motion of your foot. The can would exert a force on your foot thatis equal in magnitude but opposite in direction.

The forward force on the can would cause it to gain velocity in the direction that your foot is moving. The backward force on your foot would cause your foot to slowdown.

Equal acceleration

In the unlikely event that the mass of the can is exactly equal to the mass of your foot, the negative acceleration experienced by your foot wouldbe equal to the positive acceleration exerted on the can. That is the one case where not only the magnitudes of the forces, but also the magnitudes of theaccelerations would be equal.

For collisions between equal-mass objects, each object experiences the same acceleration.

Conservation of momentum

When two objects interact in an isolated system , the total momentum of the two objects before the interaction is equal to the total momentum of thetwo objects after the interaction. The momentum lost by one object is gained by the other object.

The total momentum of a collection of objects in a system is conserved. The total amount of momentum is constant.

Many forms of interaction are possible

There are many ways that two objects can interact. For example, when a car pulls away from a stoplight, it gains momentum by exerting frictional forces onthe surface of the earth. When that happens, the earth loses an equal amount of momentum. (Fortunately, this represents a very small fraction of the earth'smomentum, so the loss of momentum isn't noticeable.)

When the driver applies the brakes and stops the car at the next stop light (by exerting frictional forces on the surface of the earth), the car losesall of its momentum and the earth gains an equal amount of momentum. (Once again, this represents a very small fraction of the earth's momentum, so thegain of momentum isn't noticeable.)

Railroad cars and controlled collisions

Earlier in this module, I described a process where controlled collisions are used to couple railroad cars together.

While one railroad car is either standing still, or moving at a slow speed, another railroad car purposely collides with that car. When that happens, the two railroad cars become fastened together (coupled).

Distribution of momentum

Prior to the collision, each car possesses a given amount of momentum, which can be zero for a car at rest or non-zero for a car in motion. After the collision, the momentum of each car will have changed.