Title: Chapter 9: Momentum and Conservation
1Chapter 9 Momentum and Conservation
2Dynamics of Physics
- Dynamics are the CAUSES of CHANGE in Physics.
- Recall that position is changed by velocity.
- Velocity is changed by acceleration.
- Acceleration is caused by a net force.
- Properties that remain constant are described as
CONSERVED.
3Impulse and Momentum
- Momentum is described by Newtons 3 laws of
motion as the quantity of motion. - If no net force acts on a body, its velocity is
constant. - If a net force acts on a body, velocity is
changed. (acceleration) - Forces on objects change over time.
- Identify before, during, and after in an
interaction.
4Developing Impulse
- F ma can be rewritten to substitute a rate of
change in velocity for acceleration. - multiplying both sides by ?t, then
- Impulse is a force over a period of time. (Ns)
- Since a FORCE causes a velocity to CHANGE, then
an IMPULSE causes MOMENTUM to change. (kgm/s)
5Impulse-Momentum Theorem
Can also be stated as
The symbol for Momentum is ?. Thus, ? mv.
Impulse Change in Momentum The force is not
constant, and the impulse is found using the
AVERAGE FORCE times the time interval, or finding
the area under the curve of a force-time graph.
6Vectors
- Velocity is a vector, so momentum is a vector.
- Force is a vector, so impulse is a vector.
- Vectors have positive and negative directions
associated with them. Traditionally, positive
direction is right and left is negative.
7Saving lives with Physics
- A large change in momentum comes from a large
impulse. - Since Impulse is F?t, you can have a large force
OR a large time of contact to produce a large
impulse. - In a car crash, an air bag extends the TIME of
contact to reduce the FORCE of impact. The
Impulse is the same whether you hit the air bag,
or the steering wheel. Thus the ?mv is the same. - Car crash video clip
- Car crash with seatbelts
8Angular Momentum
- Just like linear momentum is mv, a ROTATING
object has momentum also. The momentum of a
rotating object is called Angular Momentum and
depends on the objects mass, distance from the
center axis of rotation, and tangential velocity.
If the radius gets smaller, the velocity
increases to maintain constant angular momentum.
Like water going down the toilet, or a hurricane,
or planets around a star (sun).
9Practice Problem
- A 0.144kg baseball is pitched horizontally at
38.0m/s. After it is hit by the bat, it moves at
the same speed, but in an opposite direction. - What was the change in momentum of the ball?
- What was the impulse delivered by the bat?
10Batter Up Solution
- Given mball 0.144kg, v38.0 m/s, direction
direction after ball leaves bat - Unknown F?t ??
- Solve
- ?? mv2-mv1 m(v2 v1)
- (0.144kg)(38.0m/s-(-38.0m/s))
- (0.144kg)(76.0m/s) 10.9 kg-m/s
- Impulse change in momentum
- 10.9 N-s
11Your turn to practice
- Do pg. 204-205 Practice Problems 1,2,3,4,5,6
- Do pg.217 s 1,2,4,6,7
- Do pg. 218 s 22-27
12Conservation of Momentum
- Forces are a result of an interaction between
objects moving in opposite directions. - During collisions, the force of one object on
another is in strength but opposite in
direction to the force of the second object on
the first. - The time interval for the force is the same for
both objects, so the Impulse is and opposite.
13What about Momenta?
- According to the I-M theorem, the final momentum
the impulse the initial momentum. - In a collision, the final momenta must be equal
to the sum of the initial momenta in a system and
thus Momentum is Conserved.
14Defining Closed Systems
- A system that doesnt gain or lose mass is said
to be a closed system. - All forces within a closed system are called
internal forces. - All forces outside a closed system are considered
external forces. - In a system, objects that collide can either
stick together (inelastic collision), or come
apart (elastic collision). Momentum of the
collision in a closed system with no net external
force is still conserved.
15Car collision problem
- A 2275kg car going 28m/s rear-ends an 875kg
compact car going 16m/s on ice in the same
direction. The cars stick together. How fast
does the wreckage move after the collision?
16Car crash solution
Because the cars stick together, their velocities
after the collision are equal. So, vA2 vB2
v2 mAvA1 mBvB1 (mAmB)v2 So v2 25 m/s,
as we can see when mass increases, velocity must
decrease to conserve momentum.
17Explosions
- As with the 2 skaters in Fig 9-8, if they both
start at rest and A gives B a push, both skaters
will move in opposite directions. The push is an
internal force. The total momentum of the system
must be zero after the push as it was zero before
the push. The momenta of the skaters will be
equal and opposite after the push. - The chemicals in a rocket exploding to propel the
rocket are internal forces as they are expelled
into space propelling the rocket along. - mAvA2 -mBvB2
18Ch 9 Homework
- Please complete the following
- Pg. 210 Prac. Probs. 7,8,9, 12
- Pg. 218 Rev s 28,34,35, and 36.