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Chapter 7: Linear Momentum
Momentum: a measure of motion
Force: a cause of change in motion
What changes when a force is applied?
F  ma  m
F
v
; but mass does not change
t
mv
; mv changes with time
t
Linear Momentum: p = mv (vector!!!!!)
the tendency of an object to pursue straight line motion
Kinetic Energy in terms of momentum:
p2
KE 
2m
Phys 250 Ch7 p1
Impulse: the change in motion


J  p  mv
 
since v  at


and F  ma



J  Ft  p  mv
Example: A baseball with mass 0.14 kg and an initial speed of 30 m/s his hit with a bat and
then rebounds in the opposite direction at a speed of 40 m/s. The bat and ball are in contact for
0.0020 s. Determine the size of the impulse on the ball and the magnitude of the average force
of the bat on the ball.
Phys 250 Ch7 p2
Example: A 51 kg teenager jumps to the ground from a chair 0.34 m high. She bends her
knees slightly on landing, lowering herself by only 8.0 cm during her landing. What is the
average force with which her feet hit the ground?
Phys 250 Ch7 p3
Conservation of momentum
two bodies + action/reaction + no other forces
FAB = - FBA
=> equal but opposite impulses
=> pA + pB = 0
When the net external force on a system is zero, the total momentum of that system is
constant.
p1 + p2 + p3 + ...
is constant
Collisions: m1v1 + m2v2 =m1v’1 + m1v’2
Phys 250 Ch7 p4
Example: A Buick Park Avenue (m=1660 kg) with an initial speed of 8.0 km/hr collides head on with a Geo Metro
(m=830 kg). As a result of the collision, the cars become entangled and so “sick together”.
- What is the speed of the wreckage just after the collision?
- How do the accelerations of each car compare? (look at the changes in their velocities)
Example: A 60 kg ice skater initially at rest throws a 2 kg block of ice horizontally with a speed of 12 m/s. What is his
recoil velocity?
Ballistic Pendulum demo
Phys 250 Ch7 p5
Collisions
Elastic Collisions
conserve KE (total KE is same before and after collision)
Inelastic Collisions
some KE is lost during collision (heat, sound, etc.)
Completely Inelastic Collisions
objects stick together
maximum possible loss of KE
In all collisions, the total momentum is conserved!
Phys 250 Ch7 p6
Collisions: m1v1 + m2v2 =m1v’1 + m1v’2
in 2 or 3 dimensions: take components!
m1vx1 + m2vx2 =m1v’x1 + m1v’x2
m1vy1 + m2vy2 =m1v’y1 + m1v’y2
Example: Two cars approach an intersection at right angles. After the crash they stick together. If one
car has a mass of 1450 kg and is traveling north at 11.5 m/s and the other has a mass pf 1750 kg and is
traveling east at 15.5 m/s, determine the speed and direction of motion of the wreckage just after the
collision.
Phys 250 Ch7 p7
Example: A billiard ball moving at 10 m/s along the positive x axis collides with an identical
billiard ball at rest. After the collision, the incoming ball moves at a speed of 7.7 m/s at an
angle 40º from the x axis. What is the speed and direction of the struck ball?
Phys 250 Ch7 p8