PHYSICS 231 INTRODUCTORY PHYSICS I

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PHYSICS 231INTRODUCTORY PHYSICS I

• Lecture 8

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Last Lecture
Fx

• Work for nonconstant force
• Spring force
• Potential Energy of Spring
• Power

x
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Chapter 6

• Momentum and Collisions

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Momentum
Definition
Newtons 2nd Law
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Conservation of Momentum
True for isolated particles (no external
forces) Proof
Recall F12-F21, (Newtons 3rd Law)
for isolated particles never changes!
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Momentum is a Vector quantity

• Both Spx and Spy are conserved

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Example 6.1
An astronaut of mass 80 kg pushes away from a
space station by throwing a 0.75-kg wrench which
moves with a velocity of 24 m/s relative to the
original frame of the astronaut. What is the
astronauts recoil speed?
0.225 m/s
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Center of mass does not accelerate
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Example 6.2
Ted and his ice-boat (combined mass 240 kg)
rest on the frictionless surface of a frozen
lake. A heavy rope (mass of 80 kg and length of
100 m) is laid out in a line along the top of the
lake. Initially, Ted and the rope are at rest. At
time t0, Ted turns on a wench which winds 0.5 m
of rope onto the boat every second. a) What is
Teds velocity just after the wench turns on? b)
What is the velocity of the rope at the same
time? c) What is the Teds speed just as the rope
finishes? d) How far did the center-of-mass of
Tedboatrope move e) How far did Ted move? f)
How far did the center-of-mass of the rope move?
0.125 m/s -0.375 m/s 0 0 12.5 m -37.5 m
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Example 6.3
A 1967 Corvette of mass 1450 kg moving with a
velocity of 100 mph ( 44.7 m/s) slides on a
slick street and collides with a Hummer of mass
3250 kg which is parked on the side of the
street. The two vehicles interlock and slide off
together. What is the speed of the two vehicles
immediately after they join?
13.8 m/s 30.9 mph
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Impulse
Useful for sudden changes where the exact details
of the force are difficult to determine
For nonconstant F, Impulse Area under F vs. t
curve
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Bungee Jumper Demo
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Example 6.4

• A pitcher throws a 0.145-kg baseball so that it
  crosses home plate horizontally with a speed of
  40 m/s. It is hit straight back at the pitcher
  with a final speed of 50 m/s.
• a) What is the impulse delivered to the ball?
• b) Find the average force exerted by the bat on
  the ball if the two are in contact for 2.0 x 103
  s.
• c) What is the acceleration experienced by the
  ball?

a) 13.05 kg?m/s b) 6,525 N c) 45,000 m/s2
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Collisions

• Momentum is always conserved in a collision
• Classification of collisions
• ELASTIC
• Both energy momentum are conserved
• INELASTIC
• Momentum conserved, not energy
• Perfectly inelastic -gt objects stick
• Lost energy goes to heat

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Examples of Perfectly Inelastic Collisions

• Catching a baseball
• Football tackle
• Cars colliding and sticking
• Bat eating an insect

Examples of Perfectly Elastic Collisions

• Superball bouncing
• Electron scattering

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Ball Bounce Demo
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Example 6.5a
A superball bounces off the floor,
A) The net momentum of the earthsuperball is
conserved B) The net energy of the
earthsuperball is conserved C) Both the net
energy and the net momentum are conserved D)
Neither are conserved
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Example 6.5b
A astronaut floating in space catches a baseball
A) Momentum of the astronautbaseball is
conserved B) Mechanical energy of the
astronautbaseball is conserved C) Both
mechanical energy and momentum are conserved D)
Neither are conserved
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Example 6.5c
A proton scatters off another proton. No new
particles are created.
A) Net momentum of two protons is conserved B)
Net kinetic energy of two protons is conserved C)
Both kinetic energy and momentum are conserved D)
Neither are conserved
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Perfectly Inelastic collision in 1-dimension

• Final velocities are the same

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Example 6.6
A 5879-lb (2665 kg) Cadillac Escalade going 35
mph smashes into a 2342-lb (1061 kg) Honda Civic
also moving at 35 mph15.64 m/s in the opposite
direction.The cars collide and stick.
a) What is the final velocity of the two
vehicles? b) What are the equivalent
brick-wall speeds for each vehicle?
a) 6.73 m/s 15.1 mph b) 19.9 mph for Cadillac,
50.1 mph for Civic
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Example 6.7
A proton (mp1.67x10-27 kg) elastically collides
with a target proton which then moves straight
forward. If the initial velocity of the
projectile proton is 3.0x106 m/s, and the target
proton bounces forward, what are a) the final
velocity of the projectile proton? b) the final
velocity of the target proton?
0.0 3.0x106 m/s
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Elastic collision in 1-dimension

• Conservation of Energy
• Conservation of Momentum
• Rearrange both equations and divide

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Elastic collision in 1-dimension

• Final equations for head-on elastic collision
• Relative velocity changes sign
• Equivalent to Conservation of Energy

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Example 6.8
An proton (mp1.67x10-27 kg) elastically collides
with a target deuteron (mD2mp) which then moves
straight forward. If the initial velocity of the
projectile proton is 3.0x106 m/s, and the target
deuteron bounces forward, what are a) the final
velocity of the projectile proton? b) the final
velocity of the target deuteron?
vp -1.0x106 m/s vd 2.0x106 m/s Head-on
collisions with heavier objects always lead to
reflections
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Example 6.9a
The mass M1 enters from the left with velocity v0
and strikes the mass M2M1 which is initially at
rest. The collision is perfectly elastic.

a) Just after the collision v2 ______ v0.
A) gt B) lt C)
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Example 6.9b
The mass M1 enters from the left with velocity v0
and strikes the mass M2M1 which is initially at
rest. The collision is perfectly elastic.
Just after the collision v1 ______ 0.
A) gt B) lt C)
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Example 6.9c
The mass M1 enters from the left with velocity v0
and strikes the mass M2M1 which is initially at
rest. The collision is perfectly elastic.
Just after the collision P2 ______ M1v0.
A) gt B) lt C)
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Example 6.9d
The mass M1 enters from the left with velocity v0
and strikes the mass M2M1 which is initially at
rest. The collision is perfectly elastic.
At maximum compression, the energy stored in
the spring is ________ (1/2)M1v02
A) gt B) lt C)
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Example 6.9e
The mass M1 enters from the left with velocity v0
and strikes the mass M2ltM1 which is initially at
rest. The collision is perfectly elastic.
Just after the collision v2 ______ v0.
A) gt B) lt C)
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Example 6.9f
The mass M1 enters from the left with velocity v0
and strikes the mass M2ltM1 which is initially at
rest. The collision is perfectly elastic.
Just after the collision v1 ______ 0.
A) gt B) lt C)
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Example 6.9g
The mass M1 enters from the left with velocity v0
and strikes the mass M2ltM1 which is initially at
rest. The collision is perfectly elastic.
Just after the collision P2 ______ M1v0.
A) gt B) lt C)
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Example 6.9h
The mass M1 enters from the left with velocity v0
and strikes the mass M2ltM1 which is initially at
rest. The collision is perfectly elastic.
At maximum compression, the energy stored in
the spring is ________ (1/2)M1v02
A) gt B) lt C)
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Example 6.9i
The mass M1 enters from the left with velocity v0
and strikes the mass M2gtM1 which is initially at
rest. The collision is perfectly elastic.
Just after the collision v2 ______ v0.
A) gt B) lt C)
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Example 6.9j
The mass M1 enters from the left with velocity v0
and strikes the mass M2gtM1 which is initially at
rest. The collision is perfectly elastic.
Just after the collision v1 ______ 0.
A) gt B) lt C)
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Example 6.9k
The mass M1 enters from the left with velocity v0
and strikes the mass M2gtM1 which is initially at
rest. The collision is perfectly elastic.
Just after the collision P2 ______ M1v0.
A) gt B) lt C)
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Example 6.9l
The mass M1 enters from the left with velocity v0
and strikes the mass M2gtM1 which is initially at
rest. The collision is perfectly elastic.
At maximum compression, the energy stored in
the spring is ________ (1/2)M1v02
A) gt B) lt C)