Momentum
Introduction of a new
“quantity of motion”
Quantities of Motion
❏ We know about kinetic energy:
❏ Moving objects also have something called momentum
❏ Vector
❏ Units?
Examples
❏ Calculate the magnitudes of the following momenta
❏ 2000 kg car traveling at 30 m/s
❏ 150 g baseball traveling at 40 m/s
❏ 65 kg sprinter running at 10 m/s
Relationship Between K and p
❏ Force causes acceleration
❏ Acceleration changes velocity (speed or direction)
❏ Changes in speed change K and p simultaneously
❏ K and p are probably related
❏ To find one in terms of the other
NOT on the equation sheet
❏ Don’t increase at the same rate with increasing v
❏ p increases linearly
❏ K increases quadratically
Changing Energy
❏ Recall: Energy is changed or created by doing work
❏ Work was a force over a distance
Changing Momentum
❏ A force can also create/change momentum
❏ By how much?
❏ Consider a net force Fnet as in N2L
**On equation sheet
❏ Momentum is changed when Fnet acts over time
❏ Another unit for momentum?
Impulse
❏ A force exerted over a time interval is called an impulse
❏ Another way to say “change in momentum”
❏ The book uses J for impulse
❏ Also a vector
❏ J is parallel to F (and acceleration)
❏ NOT necessary parallel to initial momentum
❏ Depends on whether object speeds up or slows down
❏ Equivalent of “work” for momentum
❏ Calculates change in p rather than change in K
❏ We’ll have to be careful about vectors with momentum
❏ Can be calculated via the “cause” or the “effect”
Example
❏ What is the impulse on a 2000 kg car that feels a force
of 10,000 N for 5 s?
❏ What is the final speed of the car if it begins at rest?
❏ What is the final speed of the car if it experiences
another identical impulse?
Example
❏ What is the impulse experienced by a 45 m/s fastball
(m = 0.15 kg) that comes to rest in the catcher’s mitt?
❏ If the ball takes 0.005 s to stop in the glove, how large
of a force is exerted on it?
❏ What direction is the force pointing?
❏ What can we say about the force back on the glove?
Why Are Airbags Good?
❏ Who experiences a greater impulse during a car crash
from 30 m/s?
❏ Person with airbag
❏ Equal mass person without airbag
❏ Who feels a greater force during a car crash?
❏ Person with airbag
❏ Person without airbag
If Impulse is Like Work...
❏ Work = area under Force vs Distance curve
❏ Impulse = area under Force vs Time curve
❏ What is the total impulse felt by the
15 kg object subject to the plotted
force?
❏ What is the final momentum of the
object if it began at rest?
❏ What is the final momentum of the
object if pi = -20 Ns?
Example
❏ A 150 g baseball is thrown with a speed of 20 m/s. It is hit straight
back toward the pitcher at a speed of 40 m/s. The force on the ball
(from the bat) is shown shown.
❏
❏
❏
❏
❏
What is the Δp experienced by the ball?
What maximum force, Fmax, does the bat exert on the ball?
What is the average force, Favg,of the bat on the ball?
What direction is the force on the ball?
On the bat?
Demo
❏ Bouncing off of a block
Homework
❏ On Blackboard
❏ Exit tickets
General Forces
❏ Many forces change size
over a time interval
❏ Calculating impulse requires
calculus
❏ Average forces are simpler
and give the same result
❏ Assume a constant
magnitude
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