Transcript Chapter_9b

Chapter 9: Linear Momentum and
Collisions
Reading assignment: Chapter 10.1-10.5
Homework #16 :
Problems:
(due Monday, Oct. 10, 2005):
Q1, Q14, 9, 14, 21, 28
• Momentum


p  mv
• Momentum is conserved – even in collisions with energy
loss due to friction/deformation.
• Impulse
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”: J  p  p f  pi
During a collision, a force F acts on
an object, thus causing a change in
momentum of the object:
For a constant (average) force:
tf


p  J   ______ dt
ti
 
p  J  Favg  ___
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.
Black board example 10.1
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?
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)
 
pi  p f



m1v1i  m2v2i  (________)v f
Notice that p and v are
vectors and, thus have a
direction (+/-)
K i  Eloss  K f
1
1
1
2
2
2
m1v1i  m2v2i  Eloss  (_______)v f
2
2
2
There is a loss
in kinetic
energy, Eloss
Perfectly _________ collision of two particles
(Particles bounce off each other without loss of energy.
Momentum is ____________:




m1v1i  m2 v2i  m1v1 f  m2 v2 f
Energy is _____________:
1
1
1
1
2
2
2
2
m1v1i  m2 v2i  m1v1 f  m2 v2 f
2
2
2
2
For elastic collisions in
:
Suppose we know the initial masses and velocities.
Then:
 m1  m2 
 ____ 
v1i  
v2i
v1 f  
 m1  m2 
 m1  m2 
(10.38)
 ____ 
 m2  m1 
v1i  
v2i
 
 m1  m2 
 m1  m2 
(10.39)
v2 f
(10.30)
(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)
Conservation of momentum:




m1v1i  m2 v2i  m1v1 f  m2 v2 f
Split into components:
m1v1ix  m2v2ix  m1v1 fx  m2v2 fx
m1v1iy  m2v2iy  m1v1 fy  m2v2 fy
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
(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).
??? 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 (mk = 0.5)