Download Chapter 6: Momentum and Collisions

Chapter 6:
Momentum and
Collisions
Coach Kelsoe
Physics
Pages 196–227
Section 6–1:
Momentum and
Impulse
Coach Kelsoe
Physics
Pages 198–204
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
• Consider a soccer player heading a kick.
• So far the quantities and kinematic equations
we’ve introduced predict the motion of an
object, such as a soccer ball, before and after
it is struck.
• What we will consider in this chapter is how
the force and duration of the collision of an
object affects the motion of the ball.
Linear Momentum
• The linear momentum of an object of mass m
moving with a velocity v is defined as the
product of the mass and velocity.
• Momentum is represented by the symbol “p,”
which was given by German mathematician
Gottfried Leibniz, who used the term
“progress.”
• In formula terms: p = mv
Linear Momentum
• Momentum is a vector quantity, with its
direction matching that of the velocity.
• The unit for momentum is kilogram-meters
per second (kg·m/s), NOT a Newton, which
are kilogram-meters per square seconds
(kg·m/s2).
• The physics definition for momentum conveys
a similar meaning to the everyday definition
for momentum.
Sample Problem A
• A 2250 kg pickup truck has a velocity of 25
m/s to the east. What is the momentum of the
truck?
Sample Problem Solution
• Identify givens and unknowns:
– m = 2250 kg
– v = 25 m/s east
• Choose the correct formula:
– p = mv
• Plug values into formula:
– p = (2250 kg)(25 m/s east)
– p = 56,000 kg·m/s to the east
Changes in Momentum
• A change in momentum is closely related to
force. You know this from experience – it
takes more force to stop something with a lot
of momentum than with little momentum.
• When Newton expressed his second law of
motion, he didn’t say that F = ma, but instead,
he expressed it as F = Δp/Δt.
• We can rearrange this formula to find the
change in momentum by saying Δp = FΔt.
Impulse-Momentum Theorem
• The expression Δp = FΔt is
called the impulsemomentum theorem.
• Another form of this
equation that can be used is
Δp = FΔt = mvf – mvi.
• The impulse component of
the equation is the FΔt.
This idea also helps us
understand why proper
technique is important in
sports.
Sample Problem 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 0.30 s. Find the force
exerted on the car during the collision.
Sample Problem Solution
• Identify your givens and unknowns:
– m = 1400 kg
– Δt = 0.30 s
–F=?
vi = 15 m/s west or -15 m/s
vf = 0 m/s
• Choose the correct equation:
– FΔt = mvf – mvi  F = mvf – mvi/Δt
• Plug values into equation:
– F = mvf – mvi/Δt
– F = (1400 kg)(0 m/s) – (1400 kg)(-15 m/s)/0.30 s
– F = 70,000 N to the east
Impulse-Momentum Theorem
• Highway safety engineers
use the impulse-momentum
theorem to determine
stopping distances and safe
following distances for cars
and trucks.
• For instance, if a truck was
loaded down with twice its
mass, it would have twice
as much momentum and
would take longer to stop.
Sample 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?
Sample Problem Solution
• Identify givens and unknowns:
–
–
–
–
m = 2240 kg
vi = 20.0 m/s west or -20.0 m/s
vf = 5.00 m/s west or -5.00 m/s
F = 8410 N east or +8410 N
Δt = ?
Δx = ?
• Choose the correct formulas:
– FΔt = Δp  Δt = Δp/F
– Δt = mvf - mvi/F
• Plug values into formula:
– Δt = (2240 kg)(-5.00 m/s) – (2240 kg)(-20.0 m/s)/8410 N
– Δt = 4.00 s
Reducing Force
• We can reduce the force an object
experiences by increasing the stop time.
• It’s the same idea behind catching a water
balloon or an egg. The change is momentum
is the same.
• The reason this works is that time and force
are indirectly proportional. As one increases,
the other decreases.
• It’s the difference between a bunt or a
homerun!
Scrambled Eggs, Anyone?