Transcript Momentum and Collisions

Momentum and Collisions
Momentum and Impulse
Section Objectives
• Compare the momentum of different
moving objects.
• Compare the momentum of the same
object moving with different velocities.
• Identify examples of change in the
momentum of an object
• Describe changes in momentum in
terms of force and time.
Linear Momentum
• Momentum is defined as a product of
the mass and the velocity of an object.
• Momentum is mass times velocity.
– Momentum is represented by the symbol, p
– p = mv
• Momentum has the SI units of kg•m/s
• Momentum is a vector quantity.
• Clip 324
Practice Problems A
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A 2250 kg pickup truck has the velocity of
25 m/s to the east. What is the momentum
of the truck?
A 21 kg child on a 5.9 kg bike is riding with
a velocity of 4.5 m/s to the northwest.
a) What is the total momentum of the child and the
bike together?
b) What is the momentum of the child?
c) What is the momentum of the bike?
Force and Impulse
• A change in momentum takes force and
time.
– Ball example
– Bowling Ball
• From these examples we see that
change in momentum is closely related
to force.
Impulse-momentum Theorem
• Force X time interval = Change in momentum
• Ft = p = mvf - mvi
• Ft is called the impulse
• Force is reduced when the time interval of an
impact is increased.
• clip 598
Sample Problems B
• A 1400 kg car moving westward with a
velocity of 15 m/s collides with a utility pole
and is brought to rest in .30 s. find the force
exerted on the car during the collision.
• A 0.050 kg football is thrown with a velocity of
15 m/s to the right. A stationary receiver
catches the ball and brings it to rest in .020 s.
What is the force exerted on the ball by the
receiver?
Stopping Times and Distances
• Stopping times and distances depend
on the impulse-momentum. A truck with
twice the mass will take twice the
distance and time to stop.
Practice Problem C
• A 2240 kg car traveling to the west slows
down uniformly from 20.0 m/s to 5.00 m/s.
How long does it take the car to decelerate if
the force on the car is 8410 N to the east?
How far does the car travel during the
deceleration?
• How long would the car in the above sample
problem take to come to a stop from its initial
velocity of 20.0 m/s to the west? How far
would the car move before stopping? Assume
a constant acceleration.
Homework
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P 199 1, 3
P 201 2, 3, 4
P 203 2, 3
P 204 1, 2, 3
P 223 1-3, 5 -7, 11 -14
Conservation of Momentum
Section Objectives
• Describe the interaction between two objects
in terms of the change in momentum of each
object.
• Compare the total momentum of the two
objects before and after they interact.
• State the law of conservation of momentum
• Predict the final velocities of objects after
collisions, given the initial velocities.
Momentum is conserved
• This figure shows a
stationary billiard ball set into
motion by a collision with a
moving billiard ball.
• Before the collision, the
momentum of the green ball
is zero.
• During the collision the blue
ball losses momentum while
the green ball gains.
• The momentum the blue ball
losses is equal to the
momentum gained to the
green ball.
Conservation con’t
• In other words:
• Total initial momentum = total final momentum
• (m1v1)I + (m2v2)I = (m1v1)f + (m2v2)f
• For an isolated system, law of consevation of
momentum can be stated as follow:
– The total momentum of all objects interacting with
one another remains constant regardless of the
nature if the forces between the objects.
Practice Problem D
• A 76 kg boater, initially at rest in a stationary 45 kg
boat, steps out of the boat and onto the dock. If the
boater moves out of the boat with a velocity of 2.5
m/s to the right, what is the final velocity of the boat?
• A 63.0 kg astronaut is on a spacewalk when the
tether line to the shuttle breaks. The astronaut is able
to throw a spare 10.0 kg oxygen tank in a direction
away from the shuttle with a speed of 12.0 m/s,
propelling the astronaut back to the shuttle, find the
astronaut’s final speed with respect to the shuttle
after the tank is thrown.
Homework
• P 209 2, 3, 4
• P 211 1 - 3
• P 224 15 - 23
Elastic and Inelastic Collisions
Section Objectives
• Identify different types of collisions
• Determine the changes in kinetic energy
during perfectly inelastic collisions.
• Compare conservation of momentum and
conservation of kinetic energy in perfectly
inelastic and elastic collisions.
• Find the final velocity of an object in perfectly
inelastic and elastic collisions.
Inelastic Collisions
• When two objects,
such as the two
football players,
collide and move
together as one
mass, the collision is
called a perfectly
inelastic collision.
• See 327
Inelastic Collisions con’t
• Inelastic collisions are easy to analyze
in terms of momentum because the
objects become essentially one object
after the collision.
• (m1v1)i + (m2v2)i = (m1 +m2)vf
Sample Problems E
• A 1850 kg luxury sedan stopped at a traffic light is
struck from the rear by a compact car with the mass
of 975 kg. The two cars become entangled as a
result of the collision. If the compact car was moving
at the velocity of 22.0 m/s to the north before the
collision, what is the velocity of the entangled mass
after the collision?
• A grocery shopper tosses a 9.0 kg bag of rice into a
stationary 18.0 kg grocery cart. The bag hits the cart
with a horizontal speed of 5.5 m/s towards the front of
the cart. What is the final speed of the cart and the
bag?
Kinetic energy and Collisions
• In an inelastic collision, kinetic energy is
not conserved.
• The amount of kinetic energy lost can
be calculated by finding the change of
kinetic energy.
Sample Problems F
• Two clay balls collide head-on in a perfectly inelastic
collision. The first ball has a mass of 0.50 kg and an
initial velocity of 4.0 m/s to the right. The second ball
has a mass of 0.25 kg and an initial velocity of 3.0
m/s to the left. What is the decrease in kinetic energy
during the collision?
• During practice, a student kicks a 0.40 kg soccer ball
with a velocity of 8.5 m/s to the south into a 0.15 kg
bucket lying on its side. The bucket travels with the
ball after the collision.
– What is the final velocity of the combined mass?
– What is the decrease in kinetic energy during the
collision?
Elastic Collisions
• An elastic collision occurs
when two objects collide
and return to their original
shapes with no loss of total
kinetic energy.
• Kinetic energy and
momentum is conserved
in elastic collisions.
– m1v1,i + m2v2,i = m1v1,f + m2v2,f
– 1/2m1v1,i2 + 1/2m2v2,i2 = 1/2m1v1,f2+ 1/2m2v2,f2
• Clip 600
Sample Problem G
• A 0.015 kg marble moving to the right at
0.225 m/s makes an elastic head-on collision
with a 0.030 kg shooter moving to the left at
0.180 m/s. After the collision, the smaller
marble moves to the left at 0.315 m/s.
Assume hat neither marble rotates before or
after the collision and that both marbles are
moving on a frictionless surface, What is the
velocity of the 0.030 kg marble after the
collision?
Homework
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P 214 1, 3, 4, 5
P 216 1, 3
P 219 1 - 4
P 220 1 - 5
P 224 24 - 34