Center of Mass for a system of particles
Lecture 13
2 bodies, 1 dimension
Momentum Conservation
And Collisions
0
(HR&W, Chapters 9)
COM
http://web.njit.edu/~sirenko/
Physics 105 Summer 2006
Lecture 13
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Lecture 13
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Impulse and Linear Momentum
Linear Momentum
Definition of Impulse
Particle:
System of Particles:
Extended objects:
Impulse–Linear
Momentum Theorem
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Conservation of Linear Momentum
TODAY:
• Collisions
• Impulse and Linear Momentum
– Single Collision
• Momentum and Kinetic Energy
• Inelastic Collisions in One Dimension
Even if there are internal forces inside the system
– One-Dimensional Collision
– Completely Inelastic Collision
If no net external force acts on a system of particles, the total linear
momentum P of the system cannot change
If the component of the net external force on a closed system is zero
along an axis, then the component of the linear momentum along
that axis cannot change
• Elastic Collisions in One Dimension
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Collision of two particle-like bodies
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Elastic Collisions in 1D
In an elastic collision, the kinetic energy of each colliding body may
change, but the total kinetic energy of the system does not change
Stationary Target
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Moving Target
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Elastic Collisions in 1D
Elastic Collisions in 1D
???
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What is the rebound
heights of the Basketball ?
What is the rebound
heights of the tennis ball ?
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Elastic and Inelastic
Collisions
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h=1m
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Inelastic Collisions in 1D
Conservation of Linear
Momentum
Kinetic Energy is not conserved
Cannot solve based only on the information about the state
before the collision
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Completely Inelastic Collision
Collisions in 1D
Inelastic Collisions in 1D
Conservation of Linear
Momentum works !
Velocity of Center of Mass
Half the original
Kinetic Energy
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Which way should I shoot the trashcan to
make it go faster ???
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Who wins ?
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Light pressure
How can we reach another star ?
Combination of
¾Regular rocket
¾Ion-drive engine
¾And Solar sail
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Sample Problem
Ballistic Pendulum.
Pendulum. A bullet is fired
into the block (M
(M = 5 kg, m = 10 g). The
block/bullet is then swinging upward,
their center of mass rising h = 6 cm.
What is the speed of the bullet just prior
to the collision?
a) Linear Momentum is
conserved at the collision
What color/material is the best for the Light Sail?
A) Black; B) Mirror-type; C) Blue;
Lecture 13
b) After collision the Energy is
conserved
D) any
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Lecture 13
QZ#13
Linear Momentum
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Elastic Collisions in 2D
bum
The figure shows a 2.0 kg toy car before and after taking a turn on a
track. Its speed is 0.30 km/s before the turn and 0.40 km/s after the turn.
The turn takes 0.33 seconds.
(a)
What is the change ∆P in the linear momentum of the car due to
the turn?
(b)
What is the average force of friction between the car and the
road during the turn ?
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Elastic Collisions in 2D
Conservation of Linear Momentum
A firecracker placed inside a coconut of
mass M, initially at rest on a frictionless
floor, blows the coconut into three
pieces that slide across the floor. An
overhead view is shown. Piece C, with
mass 0.30 M, has final speed vfC = 5.0
m/s.
m/s.
Conservation of Linear
Momentum works !
bum
Kinetic Energy is conserved
(a) What is the speed of piece B, with mass
0.2 M ?
(b) (b) What is the speed of piece A?
com
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