PHYS16 – Lecture 21
Ch. 9 Momentum and Collisions
Ch. 9 Momentum & Collisions
• Linear Momentum
– Related to Newton’s second law
– Rocket Propulsion
• Momentum Conservation
• Collisions
– Elastic vs. Inelastic
– 1D and 2D
• Impulse
Momentum pre-question
• Consider two carts on a frictionless air track with
masses m and 2m. If you push the lower mass
cart for 3 s and then the other cart for the same
length of time and with the same force, which
cart undergoes the larger change in momentum?
A)
B)
C)
D)
Cart with mass m
Cart with mass 2m
Change in momentum is the same for both
There is not enough information
Solve Problems with Collisions
• Read problem carefully!
• Draw a picture.
• Write down given quantities and what you want
to solve for.
• Find the correct equation (conservation of
momentum and possibly conservation of energy).
• Do the math and solve!
Perfectly Elastic Collision
• A 1.00-kg ball traveling at 3.00 m/s collides with a
3.00-kg ball traveling at 0.500 m/s. If after a perfectly
elastic collision the 1.00-kg ball is traveling at -0.750
m/s, how fast is the second ball going? How do we
check to see if it is perfectly elastic?

p  0
m1v1i  m2 v2i  m1v1 f  m2 v2 f
v2 f 
m1v1i  m2 v2i  m1v1 f
m2
 1.75m/s
K  0 or check relative velocitie s
v1i  v1 f  v2 f  v2i  YES!
Perfectly Inelastic Collision
• How fast would a 5-g fly have to be traveling
to slow a 1900-kg car traveling at 55 mph to
50 mph if the fly just splatted across the
windshield?

p  0
m flyv fly  mcar vcar  (m1  m2 )vcar  fly
v fly 
(m1  m2 )vcar  fly  mcar vcar
m fly
 2E6 mph
Superball vs. Basketball
• Drop a superball and basketball together. How
high does the superball bounce?
• Homework problem…

E  0, p  0
For Problems with multiple parts…
• Follow the steps for solving problems as
before
• When you get to what equation to use break
the problem into parts – usually
chronologically – and solve each part
• Then do the math as before…
Click-Clack
• In a click-clack if all balls have equal mass and
I take one ball out and put it at height 4 m,
how high should the ball on the other side go?
A) 4 m
B) 2 m
C) 1 m
D) 0 m
E) Not enough information
http://www.brucegray.com/images/clickclack.jpg
Click-Clack
1) E  U  K  0
1
2
2
mg ( ybot  ytop )  m(vbot
 vtop
)0
2
1 2
mg ( ytop )  mvbot  0, vbot  2 gytop
2

2) p  0
mvball1i  mvball2i  mvball1 f  mvball2 f
vball1i  vbot , vball2i  0, vball1 f  0
 vball2 f  vbot  vball5 f  vbot
3) E  U  K  0
1
2
2
mg ( ytop2  ybot )  m(vtop

v
2
bot )  0
2
1 2
mg ( ytop2 )  mvbot
 0, ytop2  ytop
2
http://www.brucegray.com/images/clickclack.jpg
Click-Clack
• In a click-clack if all balls have equal mass and
I take one ball out and put it at height 4 m,
how high should the ball on the other side go?
A) 4 m
B) 2 m
C) 1 m
D) 0 m
E) Not enough information
http://www.brucegray.com/images/clickclack.jpg
Smith & Wesson
• On homework there is a problem about how
far a chair slides when a bullet gets shot into
it. What demo does this remind you of?
• What are the parts you will need to know?
2D collisions – How to solve problems
• Separate vectors into x and y components
• Solve two equations
– Conservation of momentum in x and
– Conservation of momentum in y
• If perfectly elastic get a third equation
– Conservation of energy
2D Collisions
• Need to add 2D vectors
• Assume masses of two objects equal
– Before
– After
A
B
C
2D Collisions – Predict vectors, assume
masses are equal
A
B
2D Collision problem
• A 0.25 kg hockey puck traveling at 1.5 m/s strikes a stationary
puck with the same mass. If the first puck exits at 30 degrees
and 0.75 m/s, what is the direction of the second puck?

p  0
x  mv1ix  mv1 fx  mv2 fx
y  0  mv1 fy  mv2 fy
x  mv1i  mv1 f cos(1 f )  mv2 f cos( 2 f )
y  0  mv1 f sin( 1 f )  mv2 f sin(  2 f )
2 f
  v1 f sin( 1 f ) 

 tan 
 v  v cos( ) 
1f 
 1i 1 f
1
3. Impulse
• Impulse describes the change in momentum
– Good for describing what happens during a collision




I  p   Fdt  Fave t
• Example:
– What is momentum of 0.5 kg ball dropped from 5 m
just before it hits the floor?
– If the velocity after it hits the floor is +8 m/s upward,
what is the impulse?
– If the interaction lasts 0.01 s, what was the average
Force?
During Collisions…
• Baseball
• Soccer ball
• Water balloon?
http://www.youtube.com/watch?v=pQ9NiazPYI8
http://www.youtube.com/watch?v=90VyvOhPmA0&NR=1&feature=fvwp
http://www.youtube.com/watch?v=jjE8SQG8AwI&feature=related
Discussion
• Why does an airbag reduce injury?
• What is better in bungee jumping- a stiff cable
that won’t break at high forces or a stretchy
cable?
• Why should a boxer “ride the punch” and not
stiffen her neck muscles?
Momentum pre-question
• A 0.50 kg ball accelerates from rest at 10.0 m/s2
for 2.0 s. It then collides with and sticks to a 1.0
kg ball that is initially at rest. After the collision,
how fast are the balls going?
A) 3.3 m/s
B) 6.7 m/s
C) 10 m/s
D) 15 m/s
E) None of the above.
Momentum pre-question
• Consider two carts on a frictionless air track with
masses m and 2m. If you push the lower mass
cart for 3 s and then the other cart for the same
length of time and with the same force, which
cart undergoes the larger change in momentum?
A)
B)
C)
D)
Cart with mass m
Cart with mass 2m
Change in momentum is the same for both
There is not enough information
Conclusions
• Momentum


p  mv
• Momentum Conservation

p  0
• Elastic vs. Inelastic Collisions
• Impulse

 
p  I   FNet dt