0.18 Phy1160: force and motion -- momentum, impulse, and conservation  (Page 7/14)

Railroad cars

As a child, I grew up living next to a very large railroad yard. I was accustomed to hearing the sounds of controlled collisions between railroad cars.

How railroad couples work

The devices that hold railroad cars together in a train are activated by a controlled collision. While one railroad car is either standing still, or moving at aslow speed, another railroad car purposely collides with the first car. When that happens, the two railroad cars become fastened together (coupled).

The 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 thecollision, the momentum of each car will have changed.

The conservation of momentum -- a preview

As I will explain later, (except for the conversion of some kinetic energy into other forms, such as soundenergy) the two cars coupled together will possess the total amount of momentum that was possessed by the individual cars prior to the collision. This typically meansthat one car speeds up and the other car slows down.

A change in momentum

During the time frame surrounding the instant of the collision, each car experiences a change in momentum. With sufficiently accurate measuring devices,you could measure and record the rate of change of momentum during that short time frame.

Accelerations are not necessarily equal

Although the forces experienced by the objects are equal in magnitude, the changes in velocity (accelerations) experienced by the two objects are notnecessarily equal.

The acceleration is equal to...

As we learned in an earlier module, the acceleration experienced by an object is proportional to the applied force and inversely proportionalto the mass of the object. Therefore, different masses experiencing the same magnitude of force will experience different magnitudes ofacceleration.

Kicking a lightweight aluminum can

Consider what happens when someone leaves an empty lightweight aluminum drink can on the floor and you accidently kick it with your bare foot while walkingbriskly across the room. The can exerts a force on your foot, which fortunately doesn't hurt too much because of the small mass of the can. Your foot exerts anequal and opposite force on the can that probably sends it flying across the room.

The velocity of the can changes by a large amount, going from zero to a velocity that sends it flying. Thus, the acceleration of the can is large.

The velocity of your foot, on the other hand, changes very little at the moment of impact as a result of its large mass (although your muscular reactionmight be such as to slow the foot down shortly thereafter). Thus, the magnitude of the acceleration of your foot due solely to the collision is small.

Kicking a heavy can

Now consider the same scenario except that this time, the can contains your brother's collection of rocks. In this case, the acceleration of the can due to the collision with your foot would probably be quite small, andthe (negative) acceleration of your foot due to the collision might be much larger than with the lightweight can.