Week of February 9, 1998
Lesson 5Momentum Conservation and Collisions
-Observe impulses and Momentum change
-Derive F[!]t=[!]p theorem from Newton's 2nd Law
-Use MBL to verify F[!]t=[!]p theorem experimentally
-predict interaction forces during collisions if m₁>m₁or v₁>v₂
-Use MBL to observe interaction forces
(F₁₂=-F₂₁always)
-Combine dynamic Third Law with F[!]t=[!]p to get 1D p-conservation
-Center-of-mass, 1D collisions, 2D collisions, and particle systems
Keywords: Momentum; Center Of Mass; Momentum; Collisions; Conservation Of
Momentum;
OBJECTIVES:
*Write the equations for the center of mass (c.m.) of a system and explain all
terms.
*Use the appropriate equation to find the center of mass for simple mass
distributions.
Comments: You have already learned that you stub your toe harder trying to kick
larger masses. Now imagine another unpleasant activity: catching a bowling ball.
This gets harder to do as the ball is dropped from higher places. The difficulty
depends both on the ball's mass and its velocity just before you apply the
stopping force. This force can be applied in different ways. Any winner of an egg-
throwing-and-catching contest will tell you that the way to stop an object with
the least force is to spread the stopping process out over the maximum possible
time. In this lesson, we will develop these "folk physics" observations about
force, mass, and velocity into a system of concepts and equations, and we will
establish a law of motion that is believed to be even more fundamental than the
laws from which it will be derived! The concepts are center of mass and linear
momentum; the law is called conservation of linear momentum.
If you have ever played or observed a game of pool, football, baseball, soccer,
or hockey, or have been involved in an automobile accident, then you have
some idea about the results of a collision. We are interested in studying
collisions for a variety of reasons. For example, we can determine the speed of a
bullet by making use of the physics of the collision process. We can also estimate
the speed with which an automobile was traveling before an accident by
knowing the physics of the collision process and a few other physical principles.
Physicists find collisions especially useful in determining the properties of atoms
and subatomic particles. Essentially, a particle accelerator is a device that provides
a controlled and instrumented setting for collisions between subatomic particles
so that, among other things, some of the properties of the target particle can be
studied. In studying collisions, we will make extensive use of the principle of the
conservation of linear momentum that was introduced in the preceding lesson.
If the sum of the external forces acting on the particles involved in a collision is
zero, then linear momentum is conserved in the collision. This is fortunate
since it provides a way around the analysis of the forces of interaction between
two bodies as they collide, an otherwise formidable task. Thus, the conservation-