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Ch.9 Momentum and Its
Conservation
•
9.1 Impulse and Momentum
Momentum (p): the product of the mass (m) of
an object and its velocity (v)
p = mv
An object has a greater momentum if:
1. it has a greater mass
2. it has a greater velocity
Example Problem
• A 5 kg hockey puck has a momentum of 10
kg* m/s. What is the speed of the hockey
puck?
• A ball has a momentum of 50 kg*m/s and is
thrown at a speed of 10 m/s, what is the ball’s
mass?
Impulse
• Impulse: Force times change in time
– Impulse = FΔt
– Is the result of force acting on an object over time
• Greater force = Greater impulse
• Greater time = Greater impulse
Which would have a greater
impulse, pushing the car for
2 seconds, or pushing the
car for 30 seconds?
Which would have a greater impulse, one person
pushing a car, or 3 people pushing a car?
Impulse-Momentum Relationship
• The greater the impulse, the greater the change in
momentum.
Impulse = change in momentum
FΔt = mΔv
Impulse and the change in momentum are ALWAYS linked!
Furthermore, Δv = v2 – v1 so the impulse-momentum theorem says
we can write the equation as follows'
FΔt = p2 – p1
Would you rather…
• Drive your car into a brick wall, or into a pile of hay?
WHY?
Change in momentum =
F
t
Change in momentum = F
t
– Both would have the same change in momentum to bring your
car to a stop…BUT:
• The brick wall has a greater force over a smaller period of time
• The hay has a smaller force over a greater period of time
Impulse-Momentum
Relationship in Sports
Dancers like to have a wooden floor
with some “give,” which increases
the time of impact whenever a
dancer lands. This reduces the
chance of injury.
Boxers “ride” or “roll” with punches to
reduce the force during impact by
moving with the punch.
A karate expert can break a stack of
bricks by reducing the time that the
hand is in contact with the bricks,
which increases the force.
Egg Demo!
• http://youtu.be/lPzGSjIoW7c
Example Problem
• A 5.0-kg ball has a velocity of 10 m/s
downward just before it strikes the ground
and bounces up with a velocity of 10 m/s
upward. What is the change in momentum of
the ball?
Example Problem pg. 203
• A 2200-kg sport utility vehicle traveling at 94
km/h (26 m/s) can be stopped in 21 s by
gently applying the brakes, in 5.5 s in a panic
stop, or in 0.22 s if it hits a concrete wall.
What average force is exerted on the vehicle
in each of these stops?
Sec. 9.2 Conservation of Momentum
• Law of Conservation of Momentum:
– In the absence of an external force, the momentum of
a system remains unchanged.
The momentum gained by the
cannonball, is equal and
opposite to the momentum
gained by the cannon. So the
system has not gained or lost
momentum.
Conservation of Momentum
Collisions
Net Momentum before collision = Net Momentum after collision
• Elastic Collision: A collision in which colliding objects rebound
without lasting deformation or generation of heat
– Ex: molecules of gas, billiard ball
• Inelastic Collision: A collision in which colliding objects become
distorted, generate heat, and possibly stick together.
– Ex: One car hitting another
Elastic or Inelastic?
Inelastic
If the problem does not state
object stick together or it’s an
inelastic collision always
assume an ELASTIC collision
occurred.
Elastic or Inelastic?
Elastic
Guide to solving ANY collision problem
• DRAW A PICTURE
• USE The Law of Conservation of Momentum
Total Momentum Before Collision =
Total Momentum After Collision
pbefore = pafter
Example Problem pg. 209
• A 2275-kg car going 28 m/s rear-ends an 875kg compact car going 16 m/s on ice in the
same direction. The two cars stick together.
How fast does the wreckage move
immediately after the collision?
Example Problem
• A 10.0-kg cart moving to the right with a
speed of 2.0 m/s has a head-on collision with
a 15.0-kg cart that is initially moving to the left
with a speed of 5 m/s. After the collision, the
10.0-kg cart is moving to the left with a speed
of 2.0 m/s, what is the final velocity of the
15.0-kg cart?
Example Problem pg. 212
• An astronaut at rest in space fires a thruster
pistol that expels 35 g of hot gas at 875 m/s.
The combined mass of the astronaut and
pistol is 84 kg. How fast and in what direction
is the astronaut moving after firing the pistol?
2- Dimensional Collisions
The Law of Conservation of Momentum
still applies
Example Problem pg. 215
• A 2.00-kg ball, A, is moving at a speed of 5.00
m/s. It collides with a stationary ball, B, of the
same mass. After the collision, A moves off in
a direction of 30.0 degrees to the left of its
original direction. Ball B moves off in a
direction 90.0 degrees to right of ball A’s final
direction. How fast are they moving after the
collision?
Angular Momentum
• The product of a rotating object’s moment of
inertia and angular speed about the same
axis.
L= mvr (for a point mass)
• Conservation of Angular Momentum = the net
external torque acting on an object or objects
is zero, the angular moment of the object
does not change
Angular Momentum Demo
• http://youtu.be/WnS2d24HCK0