Physics 170 - Mechanics
Lecture 21
Elastic Collisions and C.M.
1
Elastic Collisions
In elastic collisions, both kinetic energy and
momentum are conserved.
One-dimensional elastic collision:
2
Elastic Collisions in 1D
Momentum
Conservation
Energy
Conservation
Speed of approach = Speed of separation
3
Example:
Elastic Collision of Two Blocks
A 4.0 kg block moving to the right at
6.0 m/s undergoes an elastic head-on
collision with a 2.0 kg block moving to
the right at 3.0 m/s.
Find their final velocities.
2D Elastic Collisions
Two-dimensional collisions can only be solved if
some of the final information is known, such as the
final velocity of one object:
5
Summary Collisions
6
Center of Mass
The center of mass of a system is the point
where the system can be balanced in a uniform
gravitational field.
7
8
Center of Mass
For two objects:
The center of mass is closer to the more
massive object.
Note that we can also apply this relation to
the velocities and accelerations of the objects
and their center of mass.
9
Center of Mass
The center of mass need not be within the
object:
10
Motion of the Center of Mass
Motion of the center of mass:
11
Center of Mass
The center of mass is the point on (or near)
an extended object that moves as if all the mass
of the object were concentrated at that point.
x2
12
Center of Mass
The total mass multiplied by the acceleration
of the center of mass is equal to the net external
force:
The center of mass
accelerates just as
though it were a point
particle of mass M
acted on by
13
Rocket Science
A rocket engine burns fuel and
expels it from its exhaust as hot
gases. The rocket+gas system is
isolated and will have no change in
momentum: pR + pG = 0
Therefore, the rocket gains
momentum in the upward direction
by giving momentum to the “fuel
packet” that moves away at high
velocity in the downward direction.
14
Systems with Changing Mass:
Rocket Propulsion
If a mass of fuel Δm is ejected from a
rocket with speed v, the change in momentum
of the rocket is:
The force, or thrust, is
15