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Chapter 9: Linear Momentum and Collisions. Reading assignment: Chapter 10.1-10.5 Homework #16 :(due Monday, Oct. 10, 2005): Problems:Q1, Q14, 9, 14, 21, 28 . Momentum Momentum is conserved – even in collisions with energy loss due to friction/deformation. Impulse. - PowerPoint PPT Presentation
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• Momentum
• Momentum is conserved – even in collisions with energy loss due to friction/deformation.
• Impulse
Chapter 9: Linear Momentum and Collisions
vmp
Reading assignment: Chapter 10.1-10.5
Homework #16 : (due Monday, Oct. 10, 2005):
Problems: Q1, Q14, 9, 14, 21, 28
Black board example 9.3
You (100kg) and your skinny friend (50.0 kg) stand face-to-face on a frictionless, frozen pond. You push off each other. You move backwards with a speed of 5.00 m/s.
(a) What is the total momentum of the you-and-your-friend system?
(b) What is your momentum after you pushed off?
(c) What is your friends speed after you pushed off?
Impulse (change in _________________)
A change in _________ is called “impulse”: if pppJ
During a collision, a force F acts on an object, thus causing a change in momentum of the object:
f
i
t
t
dtJp ______
For a constant (average) force: ___ avgFJp
Think of hitting a soccer ball: A force F acting over a time t causes a change p in the momentum (velocity) of the ball.
A soccer player hits a ball (mass m = 440 g) coming at him with a velocity of 20 m/s. After it was hit, the ball travels in the opposite direction with a velocity of 30 m/s.
(a) What impulse acts on the ball while it is in contact with the foot?
(b) The impact time is 0.1s. What is the acting on the ball?
Black board example 10.1
Elastic and inelastic collisions in one dimension
________________ is conserved in any collision, elastic and inelastic.
___________________ is only conserved in elastic collisions.
Perfectly inelastic collision: After colliding, particles __________________. There is a loss of kinetic energy (deformation).
Inelastic collisions: Particles _________________ with some loss of kinetic energy.
Perfectly elastic collision: Particles __________________ without loss of kinetic energy.
Perfectly _____________ collision of two particles
(Particles stick together)
fii
fi
vvmvm
pp
(________)2211
Notice that p and v are vectors and, thus have a direction (+/-)
2222
211 (_______)
2
1
2
1
2
1flossii
flossi
vEvmvm
KEK
There is a loss in kinetic energy, Eloss
Perfectly _________ collision of two particles
(Particles bounce off each other without loss of energy.
ffii vmvmvmvm 22112211
222
211
222
211 2
1
2
1
2
1
2
1ffii vmvmvmvm
Energy is _____________:
Momentum is ____________:
iif
iif
vmm
mmv
mmv
vmm
vmm
mmv
221
121
212
221
121
211
____
____
For elastic collisions in :
Suppose we know the initial masses and velocities.
Then:
(10.38)
(10.30)
(10.39)
(10.31)
Black board example 9.2
Two carts collide elastically on a frictionless track. The first cart (m1 = 1kg) has a velocity in the positive x-direction of 2 m/s; the other cart (m = 0.5 kg) has velocity in the negative x-direction of 5 m/s.
(a) Find the speed of both carts after the collision.
(b) What is the speed if the collision is inelastic?
(c) How much energy is lost in the inelastic collision?
Black board example 9.5
Ballistic Pendulum:
In a ballistic pendulum a bullet (0.005 kg) is fired into a block (1.0 kg) that is suspended from a light string. The block (with the bullet stuck in it) is lifted up by 0.05 m.
(a) What is the speed of the combined bullet/pendulum right after the collision?
(b) Find the initial speed of the bullet?
(c) Find the loss in mechanical energy due to the collision
_______________ collisions (Two particles)
ffii vmvmvmvm 22112211
Conservation of momentum:
Split into components:
fyfyiyiy
fxfxixix
vmvmvmvm
vmvmvmvm
22112211
22112211
If the collision is ____________, we can also use conservation of energy.
Black board example 9.3
Accident investigation. Two automobiles of equal mass approach an intersection. One vehicle is traveling towards the east with 29 mi/h (13.0 m/s) and the other is traveling north with unknown speed. The vehicles collide in the intersection and stick together, leaving skid marks at an angle of 55º north of east. The second driver claims he was driving below the speed limit of 35 mi/h (15.6 m/s).
13.0 m/s
??? m/s
Is he telling the truth?
What is the speed of the “combined vehicles” right after the collision?
How long are the skid marks (k = 0.5)