Physics 114C Mechanics Lecture 20 Walker: Ch' 9'13 Momentum

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Physics 114C - MechanicsLecture 20 (Walker
Ch. 9.1-3)Momentum ImpulseOctober 31, 2008

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Announcements

• Homework Assignment 6 is due at 1159 PM on
  Thursday, November 6. Homework up to 24 hours
  late will receive 70 credit.
• There are now 147/166 clicker registrations.
• One week from today we will have Exam 2. The
  format will be very similar to that of Exam 1.
  In particular, there will be assigned seating.
  If you have a need or preference for a
  left-handed seat, an aisle seat, or a front-row
  seat, send me E-mail as soon as possible.

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Lecture Schedule (Part 2)
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Linear Momentum
Momentum is a vector its direction is the
same as the direction of the velocity.
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Change in Momentum
Change in momentum Dp pafter - pbefore Teddy
Bear Dp 0-(-mv) mv Bouncing Ball Dp
mv-(-mv) 2mv
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Momentum Newtons Second Law
Newtons second law, as we wrote it before
is only valid for objects that have constant
mass. Here is a more general form in terms
of momentum, also useful when the mass is
changing
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Impulse
Impulse is a vector, in the same direction as the
average force.
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Impulse
We can rewrite as So we see that The
impulse I is equal to the change in momentum Dp.
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Clicker Question 1
A 10 kg cart collides with a wall and
changes its direction. What is its change in
x-momentum Dpx?

• -30 kg m/s
• -10 kg m/s
• 10 kg m/s
• 20 kg m/s
• 30 kg m/s

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Momentum and Impulse
Microscopic view of a bounce.
Profile of the force during a collision.
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Impulse and Average Force
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Problem Solving Strategy
Picture To estimate the average force Fav, we
first estimate the impulse I of the force.
Assuming other forces are negligible, the impulse
of the force is the net impulse, which is equal
to the change in momentum, i.e., the mass times
the change in velocity. An estimate of the
velocity change Dv can be made from estimates of
the collision time Dt and displacement Dr.
Solve1. Calculate (or estimate) the impulse I
and the time Dt. This estimate assumes that
during the collision, the collision force is very
large compared to all other forces on the object.
This procedure works only if the displacement
during collision can be determined.2. Draw a
sketch showing before and after positions of the
object. Add coordinate axes and label velocities
and displacement.3. Calculate the momentum
change during the collision. (IDpmDv)4. Use
FavI/Dt to calculate the average force. Check
Average force is a vector, and should be in the
same direction as Dv.
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Impulse
Therefore, the same change in momentum may
be produced by a large force acting for a short
time, or by a smaller force acting for a longer
time.
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Example Hitting a Baseball (1)

A 150 g baseball is thrown at a speed of 20
m/s. It is hit straight back to the pitcher at a
speed of 40 m/s. The interaction force is as
shown here. What is the maximum force Fmax
that the bat exerts on the ball? What is the
average force Fav that the bat exerts on the
ball?
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Example Hitting a Baseball (2)
Use the impulse approximation Neglect
all other forces on ball during the brief
duration of the collision.
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Example A Bouncing Ball
A 100 g rubber ball is dropped from a height
of 2.0 m onto a hard floor.
The floor exertsa force on the ballas shown
above. How high does the ball bounce?
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Example A Karate Collision
With an expert karate blow, you shatter a
concrete block. Consider that you hand has a
mass of 0.70 kg, is initially moving downward at
5.0 m/s, and stops 6.0 mm beyond the point of
contact. (a) What impulse does the block exert
on your hand? (b) What is the approximate
collision time and average force that the block
exerts on your hand?
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Example A Crumpled Car
A car equipped with a 80 kg crash dummy
drives into a massive concrete wall at 25 m/s
(about 56 mi/h). (a) Estimate the displacement
of the dummy during the crash. (b) Estimate the
average force that the seat belt exerts on the
dummy.
If the front 25 of a 4.0 m long car
crumples, the displacement of the car and dummy
during the crash is about 1.0 m.
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Conservationof Linear Momentum
Momentum
Conservationof Momentum
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Problem Solving Strategy
Picture Determe that the net external force
SFext (or SFext x) on the system is negligible
for some time interval. (If the net force is NOT
determined to be negligible, do not
proceed.) Solve1. Draw a sketch showing the
system before and after the time interval.
Include coordinate axes and label the initial and
final velocity vectors.2. Equate the initial
momentum to the final momentum and express this
as a vector equation (or one or more scalar
equations involving x, y, and z components.)3.
Substitute the given information into the
equation(s) and solve for the quantity or
quantities of interest. Check Make sure you
include any minus signs that accompany velocity
components, because momentum can have either sign.
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Example A Space Repair
During repair of the Hubble Space Telescope,
an astronaut replaces a damaged solar panel
during a spacewalk. Pushing the detached panel
away into space, he is propelled in the opposite
direction. The astronauts mass is 60 kg, and
the panels mass is 80 kg. Both astronaut and
panel are initially at rest relative to the
telescope, until the astronaut gives the panel a
shove, giving it a velocity of 0.30 m/s relative
to the telescope. Assuming his tether is
slack, what is his velocity relative to the
telescope?
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ExampleA Runaway Railroad Car
A runaway 14,000 kg railroad car is rolling
horizontally ay 4.00 m/s toward a switchyard. As
it passes a grain elevator, 2,000 kg of grain
suddenly drops into the car. Assume that the
grain drops vertically and that rolling friction
and air drag are negligible. How long does
it take for the car to travel the 500 m distance
from the grain elevator to the switchyard?
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End of Lecture 20

• Before Tuesday, read Walker Chapter 9.4-5.
• Homework Assignments 6 should be submitted
  using the Tycho system by1159 PM on Thursday,
  Nov. 6. (24 hours late Þ 70 credit)
• Register your clicker, using the Clicker link
  on the Physics 114C Syllabus page.