Honors Physics
Chapter 6
Momentum
Momentum is difficult to describe, but easy to calculate.
momentum = mass x velocity
Momentum is a vector quantity.
Momentum has the same direction as the velocity.
An object must be in motion to have momentum.
Practice Problems, Page 209, 1-3
Impulse
Impulse is defined as the change in momentum.
The change in momentum can occur by a change in mass, a change in
velocity, or both.
Normally the mass of an object does not change, so an impulse describes a
change in velocity.
force is applied, the greater the change that occurs.
Impulse = force x time interval
Case 1 Impulse (increasing)
Case 1 Impulse involves increasing the momentum of an object.
When increasing the momentum, there is no limit.
Increase the force applied and extend the time the force is applied.
Case 2 Impulse (decreasing over a long time)
Case 2 Impluse involves decreasing the momentum of an object over a long
time interval.
When decreasing momentum, there is a limit.
Increasing the time of impact will decrease the force of impact.
Case 2 example:
A truck of mass 1000 kg initially moving at 20 m/s must stop.
1000 kg x 20 m/s = 20000 kg.m/s
, the force of impact is 2000 N.
Case 3 Impulse (decreasing over a short time)
Case 3 Impulse involves decreasing the momentum of an object over a short
time interval.
As in case two, there is a fixed amount of momentum to remove.
Decreasing the time of impact will increase the force of impact.
Case 3 example:
A karate expert swings his 2 kg fist at a speed of 10 m/s and hits a
wooden board and stops.
2 kg x 10 m/s = 20 kg.m/s
force of impact is 40 N.
Bouncing
Impulses are greater when bouncing takes place.
When an object bounces, it is actually a two step process:
(1) stop the object
(2) project the object back
Bouncing example:
A 2 kg ball moves toward a wall at 5 m/s. What is the impulse provided by
the wall if the ball stops? What is the impulse if the ball bounces back at 5 m/s?
2 kg x 5 m/s = 10 kg.m/s
stops, the final momentum is zero. The change in momentum is 10 kg.m/s.
bounces, the final momentum of the ball is: 2 kg x -5m/s = -10
kg.m/s So the impulse is -20 kg/m.s (from +10 to -10.)
Practice Problems, Page 211, #1-4
Practice Problems, Page 213, #103
Section Review, Page 214, #1-5
Conservation
Conservation means no net loss or gain. Whatever quantity you are
measuring remains the same.
There are three main conservation laws in physics:
Conservation of linear momentum
Conservation of energy
Conservation of angular momentum
Conservation of Momentum
For momentum to be conserved there must be no net gain or loss in
momentum. In other words, no net impulse.
For no net impulse to occur, there must be no net force acting on the system
of objects.
Internal forces are allowed, the objects can exert forces on each other.
The momentum of individual objects within the system can change, but the
net change in momentum for the system must be zero.
Conservation of momentum example:
originally at rest. If the bullet is fired at 300 m/s, what is the recoil velocity of
the rifle?
nal momentum of the rifle is: 500 grams x 0 m/s = 0
5 grams x 0 m/s = 0
0+0=0
entum of the bullet is: 5 grams x 300 m/s = 1500 g.m/s
-1500 g.m/s
- 1500 g.m/s = 500 grams x ?
– 3 m/s (The negative indicates the rifle kicks in the direction opposite to the
direction the bullet was fired.)
Practice Problems, Page 219, #1-4
Section Review, Page 221, #1-4
Collisions
A collision is the meeting or mutual striking of two or more objects.
The key word is “mutual” – the objects exert equal but opposite forces upon
each other.
The net force on the system of objects, and the net impulse, is zero.
Momentum is conserved for all types of collisions.
Elastic Collisions
A collision in which the objects rebound without lasting deformation and
without heat being produced is called elastic. Kinetic Energy is conserved in
elastic collisions (no heat is produced… very rare!)
A perfectly elastic collision is one in which the first object is originally in
motion, the second at rest, and after the collision, the first object stops, the
second begins to move.
Perfectly elastic collision example
s, collides with a 300
gram white billiard ball initially at rest. After the collision, the red billiard ball
is at rest. What is the velocity of the white billiard ball after the collision?
0 g.m/s
300 grams x 0 = 0
300 grams x ?
total momentum is 600 g.m/s, so the final velocity of the white ball must
be 2 m/s!
Inelastic Collisions
A collision in which there is a lasting deformation, heat produced, or both, is
called inelastic. (Most “real life” collisions are inelastic.)
For a perfectly inelastic collision, the objects stick together upon impact.
Perfectly inelastic collision example
yellow glider initially at rest. The gliders stick together upon collision. What is
the velocity of the combined mass after the collision?
200 grams x 4 m/s
= 800 g.m/s
the collision is 800 + 0 = 800 g.m/s
Complicated Collisions
Even very complicated collisions at angles can be calculated using the rules
for vector addition from previous chapters.
Practice Problems, Page 224, #1-5
Practice Problems, Page 226, #1-3
Practice Problems, Page 229, #1-4
Section Review, Page 230, #1-5
Chapter 6 Homework
Part 1:
1, 3, 5, 6, 7, 8, 11, 13, 14, 15
Part 2:
17, 23, 24, 28, 29, 31, 32, 35, 37, 38
Part 3:
41, 44, 47, 48, 51, 53, 56