LVang+-+Lab+12+-+Physlets+Illustration+8.1+to+8.3


 * Illustration 8.1:**

The illustration shows that if object one (m) and object two (2m) are pushed with the face force for the same interval of time, then their momentum are the same because F = rate of change in momentum, which is the same in both cases. Note, however, that each object has a different change in velocity. In fact, object one is twice as fast as object 2, which has two times the mass.

In a force vs. time graph, the integral shows impulse (change of momentum). Even with the change in mass, the impulse is still the same; thus it is wise to say that impulse is independent of mass. The force applied on the object, however, does matter:the greater the force, the greater the impulse because the force is applied for a longer period of time causing a larger change in momentum.


 * Illustration 8.2:**

This illustration notice that the change in mass of the projectile does not affect its impulse (change in momentum)m but it //does// affect the final velocity of the object. Doubling the mass (2m) reduces its velocity to half of that of the original mass (m). That being said, it's logical and visually agreeable to say that kinetic energy also changes.

Since work is related to the displacement of the object, a larger mass will accelerate slower; thus, it'll move a lesser distance and have a lower kinetic energy. When graphing a Fcos(theta) vs. distance graph, the integral will be the work, the the change in kinetic energy. Mass 2 (2m) recieves less work than the original mass (m).

When a larger force is applied to the same object, it'll result in a greater change in kinetic energy because the force is applied for a longer distance.


 * Illustration 8.3:**

The two particles in study are identical and have the same velocities.

Animation 1 shows that there is only a force, a change in acclereation, when the objects collide; until then, both particle travel at a constant velocity. Such collisions are called contact interaction. Because the acceleration is very large and the interaction is very short ranged, this interaction is characterized as "//hard//."

Animation 2 shows two particles of identical characteristics slowing down towards each other and then repelling each other into the opposite direct of their original path. Such an interaction is "//soft//" because the change in velocity is low and occurs over a long period of time. For this case, as the mass increases, its acceleration increases as well.

Despite the differences in acceleration, when the object's acceleration is multiplied by its mass, the sum of forces will turn out equal and opposite, Newton's third law. Accordingly, this means the forces will cancel out and equal zero; therefore, it the change in momentum will also be zero. It's only logical due to the law of conservation of momentum and no external force is applied to the system.