Mechanics III Momentum and Impulse
-
Upload
hunter-weiss -
Category
Documents
-
view
23 -
download
0
description
Transcript of Mechanics III Momentum and Impulse
Physics I Honors
What is Momentum?What is Momentum?It is a vector quantity that is the product of an
object’s mass and velocity.
mvWhat Are the Units?
s
mkg
Physics I Honors
What Is Momentum?
Two identical cars at different speeds…have different amounts of momentum.
Two different cars are the same speed…have different amounts of momentum.
Momentum relates to the size of the car and how fast it is moving.
That is to say, momentum is related to the car’s mass and its velocity…
Physics I Honors
P = mv
Large Momentum Examples– Huge ship moving at a small velocity
P = mv
–High velocity bullet
Physics I Honors
• A large truck has more momentum than a car moving at the same speed because it has a greater mass.
• Which is more difficult to slow down? The car or the large truck?
Momentum Examples
Physics I Honors
Here Are Some Thoughts…• Hitting a baseball or a golf ball
requires a short period of time.• Stopping a train, a ship, or a car
takes a while.
• Obviously, the train or the ship have more momentum than the baseball.
Physics I Honors
How does the object change momentum?
• Because momentum is mass x velocity, – and the mass of the object does not change, – any change in momentum means the velocity
changes.
= mv
Physics I Honors
The force that causes a change in momentum in time t, is called an impulse.
• The act of hitting a baseball or a golf ball over a period of time or stopping a train or ship or car is the impulse that changes the momentum of the ball.
• Force x time is the impulse.• Impulse causes a change in momentum. • It is a vector quantity whose direction is that of the
force.
Physics I Honors
Concept check
• What is the change in momentum of a 2 kg ball going from 3m/s to 6m/s in the same direction?
• What Impulse will cause this change?
• What force will cause this change if applies for 10 ms.?
Physics I Honors
Newton’s Second Law
• Newton’s Second Law can now be restated as the change in momentum per unit time! !
• A force is required to change momentum…• …the speed relates to how long (time) the force
must be applied!F = ma
= mv/t• So:
F t = mv
Physics I Honors
When Force is Limited• Apply a force for a long time.
– Examples: • Follow through on a golf swing.
• Pushing a car.
Ft
Physics I Honors
Maximize Momentum Change
Apply a large force for a short time.– Examples:
• Boxing
• Karate
Ft
Physics I Honors
Relation of Force and Impulse
• If forces come in equal and opposite pairs, what about Impulse?
• If Impulses are equal what is the difference caused by a bigger mass?
• Hint a 600 lb sumo wrestler and 90 lb nerd collide with equal Impulse. What difference would you observe?????
Physics I Honors
The Law of Conservation of Momentum!
• Momentum cannot be created or destroyed.• The amount of momentum in the universe is
constant.• This means that the total momentum in the system
doesn’t change.
Physics I Honors
Momentum Is Conserved!
• In a closed system, the amount of momentum before an event, such as a collision or explosion, is equal to the amount of momentum after the event, unless the system is acted upon by an outside force.
PA + PB = PA' + PB
'
Physics I Honors
Newton’s Third Law and Momentum!Newton’s Third Law and Momentum!
• When two objects collide Newton’s Third Law applies.
• Impulses are equal in magnitude but opposite in direction.
• New momentums are equal to old momentums.• Internal forces cannot cause a change in
momentum. • Momentum is conserved in all collisions that
occur in a closed, isolated system.
Physics I Honors
Momentum and Collisions Elastic Collisions
– objects rebound
– Momentum is conserved
– Kinetic energy is conserved
Inelastic Collisions – object stick together an usually become distorted and
generate heat
– Momentum is conserved
– Kinetic energy is not conserved
Physics I Honors
Elastic Collisions
Conserve Energy and Momentum
Case 1:
Case 2:
Equal masses
M > M
Case 3: M < M
Before Collision
After Collision
Physics I Honors
Inelastic Collisions
• Momentum is conserved• Kinetic energy is not conserved
Before Collision
p = Mv
After Collisionp = 2Mv’
v = 10 v = 0
M M
M M
v’ = 5
Physics I Honors
quiz
• 1. What is the impulse momentum theorem?
• 2. A baseball of mass 0.14 kg is moving at +35 m/s.
• a. Find the momentum of the baseball• b. Find the velocity at which a
bowling ball, mass 7.26 kg, would have the same momentum as the baseball.
Physics I Honors
More quizzical
• Explain the difference between elastic and inelastic collisions.
• Explain the law of conservation of momentum
• Explain the law of conservation of energy
• What is their significance in studying collision?