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Linear Momentum
AP Physics
Chapter 7
Linear Momentum
7.1 Momentum and Its Relation to Force
7.1 Momentum and Its Relation to Force
Linear momentum – product of an objects mass and its velocity
Unit is a kgm/s
The quantity is only useful when discussing collisions
7-1
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7.1 Momentum and Its Relation to Force
Impulse
7-1
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7.1 Momentum and Its Relation to Force
Impulse
7-1
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7.1 Momentum and Its Relation to Force
Impulse
Or
7-1
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7.1 Momentum and Its Relation to Force
In a collision, to decrease force, we increase time of the collision
Air Bags
7-1
Consumer Report
Linear Momentum
7.2 Conservation of Momentum
7.2 Conservation of Momentum
Two kinds of collisions
1. Perfectly elastic – objects bounce apart
2. Perfectly inelastic – objects stick together
7-2
7.2 Conservation of Momentum
In reality collisions are a combination of the two.
Law of Conservation of Momentum – in a closed system, momentum is conserved in a collision
7-2
0p p
7.2 Conservation of Momentum
In an elastic collision
Direction of velocity is given by the sign of the velocity.
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0 0A A B A A A B Bm v m v m v m v
7.2 Conservation of Momentum
In an inelastic collision
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0 0( )A A B A A Bm v m v m m v
7.2 Conservation of Momentum
In an explosion
The reverse of a
Inelastic collision
7-2
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Linear Momentum
7.3 Conservation of Momentum in Collisions
7.3 Conservation of Energy and Momentum
Energy (mechanical) is conserved in an elastic collision
So
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0 0A A B A A A B Bm v m v m v m v
0 0
2 2 2 21 1 1 12 2 2 2A A B B A A B Bm v mv v m v m v
7.3 Conservation of Energy and Momentum
Any collision in which energy is lost, is considered inelastic.
7-3
Linear Momentum
7.4 Collisions in Two Dimensions
7.4 Collisions in Two Dimensions
inelastic collisions in two dimension
As always each dimension is treated independently
Then use vector addition to calculate the final answer
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0 0( )A A x B A x A B xm v m v m m v
0 0( )A A y B A y A B ym v m v m m v
x yv v v
Linear Momentum
7.5 Center if Mass
7.5 Center of Mass
Even if an object rotates there is one point that moves in the same that a particle would move if subject to the same force.
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7.5 Center of Mass
Center of mass – the point that does not rotate
Center of gravity – the point at which the force of gravity can be considered to act
7-5
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