Momentum and Energy in Collisions. A 2kg car moving at 10m/s strikes a 2kg car at rest. They stick...
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Transcript of Momentum and Energy in Collisions. A 2kg car moving at 10m/s strikes a 2kg car at rest. They stick...
Starter
A 2kg car moving at 10m/s strikes a 2kg car at rest. They stick together and move to the right at ___________m/s.
Definition of Momentum
The symbol p stands for momentum.
Momentum is the product of mass and velocity.
p = mv
Examples of calculating momentum
A 2000kg car is moving at 30m/s. What isthe momentum of the car?
p = mv = (2000kg)(30 m/s) = 60,000 kg m/s
A .1 kg bullet has a momentum of 50 kg m/s. How fast is it moving?
v = p/m = 50/.1 = 500 m/s
More Examples:
A 10kg rock and a 2 kg rock have the same momentum of 100 kg m/s. What is the speed of each rock?
Answer: For the 10kg rock: 100 = 10v, 0r v = 10m/s.
For the 2 kg rock, 100 = 2v, or v = 50 m/s.
The Vector Nature of Momentum
Momentum is a vector – it points in the same
direction as the velocity.
In one dimension, momentum pointing to the right is positive.
Momentum pointing to the left is negative.
Example:
Find the momentum of each ball. Be careful of the signs!
Answer: For the 3kg ball, p = 3(20) = 60 kg m/s
For the 10 kg ball, p = 2(-10) = -20 kg m/s
Newton’s 2nd Law in terms of Momentum
Favg = maavg = mDv/Dt = = Dp/Dt
Favg Dt = Dp
Impulse = Change in momentum
Example
This force is applied to a 3kg particle moving at 4m/s.
1. What is the impulse?Impulse = area = ½bh = ½(3)(3) =4.5Ns
2. How fast is the particle moving after 4 seconds?
Impulse = Dp I = mvf – mvi 4.5 = 3vf – 3(4) vf = 5.5 m/s
Conservation of Momentum
Momentum is Conserved for Collisions
Total momentum = Total momentum before the collision after the
collision
Pbefore = Pafter
Types of Collisions
• Elastic ( Energy and Momentum are conserved)
• Inelastic ( Only momentum is conserved)
• Note: Momentum is Always Conserved for any collision.
Completely Inelastic Collisions
• When two objects hit and stick together.• Or, the reverse of this – when one object breaks apart into two objects.
Momentum is Conserved
Total momentum = Total momentum before the collision after the collision
Pbefore = Pafter
ExampleA cannon ( mass = 500kg) fires a cannon ball ( m = 50kg) at 40m/s.How fast does the cannon move after it fires the cannon ball?
Before: Pi = 0
After: Pf = mballvball + mcannonvcannonPi = Pf
(-mballvball )/mcannon = vcannon = (-50)(40)/500 = -4 m/s
0 = mballvball + mcannonvcannon
Example
A car mass = 1kg moving at 3m/s hits another 1kg car and they stick together.How fast are they moving after they stick together?
Pi = mvi = 1(3) = 3 Pf = 2mv = 2v 2v = 3, v = 1.5 m/s
Example
A car mass = 10kg moving at 2m/s hits another 15kg car moving to the left at3m/s and they stick together. How fast are they moving after they stick together?
Pi = m1v1i + m2v2i = 10(2) + 15(-3) = -25
Pf = m1v1f + m2v2f = (m1 + m2 )vf = 25vf
-25 = 25vf vf = -25/25 = -1 m/s
Starter
A 2kg car moving at 24m/s strikes a 10kg car at rest. They stick together and move to the right at ___________m/s.
M
M
2 particle,1-D Elastic Collisions
Momentum is conserved: m1v1i + m2v2i = m1v1f + m2v2f
Energy is Conserved :
v1i + v1f = v2i + v2f
This gives you 2 equations and 2 unknowns.
Example
A 10kg ball moving to the right at 3m/s strikes a 5kg ball at rest.
Find the velocity of each ball after the collision.
m1v1i + m2v2i = m1v1f + m2v2f
10(3) + 0 = 10v1f + 5v2f
OR (1) 30 = 10v1f + 5v2f
v1i + v1f = v2i + v2f OR (2) 3 + v1f = v2f
CONTINUED………
(2) 3 + v1f = v2f
(1) 30 = 10v1f + 5v2f
The problem now is to solve two equations and two unknowns.
Sub (2) into (1) : (1) 30 = 10v1f + 5 ( 3 + v1f )
30 = 10v1f + 15 + 5v1f , 15 = 15v1f , v1f = 1 m/s
Then (2) : 3 + v1i = v2f , 3 + 1 = 4 = v2f