Take out tables.
On a separate sheet:
Make a list of every equation we’ve
already used in this class that has the
velocity term in it.
Here is your choice:
a. I toss a bullet at you.
b. I shoot a bullet at you from a gun.
Which is more dangerous to you?
Why?
Linear Momentum
&
Impulse
Linear Momentum = mass in motion
A measure of how hard it is to stop an
object.
It is like a quantity of motion.
How is it different from inertia?
Momentum (p) depends on:
mass & velocity of object.
p = mv
m in kg
v in m/s
Units are … kg m no name.
s
Momentum is a
Vector Quantity
Same direction as velocity
All Energy KE too is a scalar
Ex 1. A 2250 kg pickup truck has v =
25 m/s east. What is the truck’s
momentum?
p = mv = (2250 kg)(25 m/s)
= 5.6 x 104 kg m
s
Change in momentum - accl
occurs any time an object changes
velocity (speed or direction).
Momentum Change &
Newton’s 2nd Law
•
•
•
•
F = ma
F = m(Dv/Dt)
FDt =mDv m (vf - vi) for const mass.
FDt = Dp Impulse.
 Dp = Change in momentum
Equations of Momentum Change
• J =FDt = Dp Impulse = change momentum.
• pf – pi.
 Dp = mvf – mvi
• for velocity change with constant mass can
factor out mass you can write,
• m (vf - vi) or mDv.
Force is required to change velocity or
momentum of a body in motion.
Force must be in contact for some time.
Increased force & contact time on
object give greatest impulse Dp = mDv.
Hit a homerun needs large impulse. The
more contact time, the less force needed to
give same impulse D p.
Impulse (J) is the momentum change.
It has the same units.
kg m
s
or
Ns
It is like force but includes a contact
time component!
Ex 2. How long does it take an
upward 100N force acting on
a 50 kg rocket to increase its
speed from 100 to 150 m/s?
F = 100 N
Dv = 50 m/s
m = 50 kg
Ft = mDv
t = mDv
F
50 kg(50 m/s)
100 kg m/s2
= 25 s.
Concept: A pitcher throws a fastball to a
catcher. Who exerts a larger force on the
ball? Explain.
Concept: Explain, in terms of impulse and
momentum, how airbags help avoid injury
in a car crash.
Examples of Impulse/
Change in Momentum
• Baseball batter swinging through ball.
• Applying brakes of car over time to stop.
Ex 3. How long does it take a
250 N force to increase to
speed of a 100 kg rocket
from 10 m/s to 200 m/s?
Ft = mDv
t = mDv
F
F = 250 N
m= 100 kg
Dv =190 m/s
t = 100kg(190m/s)
250 kg m/s2. = 76 s.
Ex 4. The speed of a 1200 kg car
increases from 5 to 29 m/s in
12 s. What force accelerated
the car?
Ex 5: A 0.4 kg ball is thrown against a
wall with a velocity of 15 m/s. If it
rebounds with a velocity of 12 m/s:
a) what was its Dv?
b) What was its Dp?
Dv = vf –
v i.
-12 m/s – (15 m/s) = - 27 m/s.
Dp = mDv
= 0.4kg(27m/s)
=10.8 kg m/s
• Running with momentum. 15 min.
• https://www.youtube.com/watch?v=jLIyDf
kQcsk
• Relaxing with impulse.13 minutes.
• https://www.youtube.com/watch?v=0nOHL
Thv2mw
Understanding Car Crashes 22 min
start 8:53
http://www.youtube.com/watch?v=yUpiV2I_IRI
• Hewitt Momentum 4:20
• https://www.youtube.com/watch?v=2Fwhj
UuzUDg
Hwk read text 208 – 211
do pg 214 #1- 4 concepts
do p 211 #1 - 4. Impulse prbs.
Also worksheet
“Impulse Momentum”
Which are units of Impulse?
Nm
N/s
Ns
N/m
A ball mass 0.10 kg is dropped from 12-m. Its momentum just as
it strikes the ground is:
1.5 kgm/s
1.8 kgm/s
2.4 kgm/s
4.8 kgm/s
A 0.060-kg tennis ball, initially moving at 12 m/s, is
struck by a racquet causing it to move in the opposite
direction at a speed of 18 m/s. What is the impulse
exerted by the racquet on the ball?
0.36 kgm/s
0.72 kgm/s
1.1 kgm/s
1.8 kgm/s
Graphs
Force N
Constant force f - t graph:
Dp /Impulse is area under curve
FDt.
Non-Constant Force
Force vs. time graph. The area under the curve =
impulse or Dp change in momentum.
What is the impulse during the 9 seconds of contact?
225 Ns
Consv Momentum Demos.
Conservation of Momentum
If no external force acts on a closed
system, the total momentum
remains unchanged even if objects
interact.
What is a system?
Two or more objects that interact
in motion. One may transfer part
or all of its momentum to the
other(s).
Common examples: collisions,
explosions.
One Ball transfers all its momentum.
The astronaut transfers part of his
momentum to the second astronaut.
Conservation of Momentum
Calc’s
• Total momentum before = total after
interactions.
• Collisions.
• Explosions
• Pushing apart.
To Calculate:
SPbefore =
Spafter
m1v1 + m2v2 = m1fv1f + m2fv2f
v1
v2 velocities for objects
one and two.
m1 and m2 masses of objects
and
Recoil From Explosions
Recoil illustrates conservation
of momentum where initial and
final momentum = 0.
0 = p1 + p2.
1. The cannon is 100kg and the
cannonball is 5 kg. If the ball leaves the
cannon with a speed of 100 m/s, find the
recoil velocity of the cannon.
Before Firing
After Firing
m1v1 + m2v2 = m1fv1f + m2fv2f
0 = (100kg)vcf + (5kg)(100m/s)
-500 kgm/s = (100 kg) vcf
- 5 m/s = vcf
recoil velocity of cannon
Extra Example – not on sheet
• A 63-kg astronaut is in spacewalk when the
tether breaks. The astronaut throws a 10-kg
oxygen tank directly away from the
spaceship at 12 m/s. Assuming the astronaut
was initially at rest, what is his final speed
after throwing the tank?
• 1.9 m/s
• Hwk. Read text p 215-218. Do pg 221 #2,
and pg 233 #17, 19, 20, 24, 25.
Recoil Hewitt 6:25
https://www.youtube.com/watch?v=1-s8NZ8xKW0
Stick em together problems
Let’s say a 4 kg fish swimming at 5 m/s,
eats a 1 kg fish. What is their final
velocity?
Bg fish sm.fish
Bg fish sm.fish
m1v1 + m2v2 = m1fv1f + m2fv2f
(4kg)(5m/s)+(1 kg)0 =(4kg)v1+(1kg)v2
But the final velocities are equal so factor out
the vf:
20 kg m/s = vf (4+1kg)
vf = (20 kg m/s) / (5kg) = 4m/s
Fish lunch Hewitt 4:00
https://www.youtube.com/watch?v=
MK0B5hEU7OI
2. A 2 kg brick is dropped on a 3 kg
cart moving at 5.0 m/s.
Find the final velocity of the
cart and brick together
cart
brick
m1v1 + m2v2 =
cart
brick
m1fv1f + m2fv2f
(3kg)(5.0m/s) + 0 = (3kg)v1 + (2kg)v2
150 kg m/s = v (3kg + 2 kg)
(150 kg m/s )/5 kg = 3.0 m/s
Elastic & Inelastic Collisions
Totally Elastic: no KE lost at all
(to heat, light, sound etc.) Usu. Involves
objects that don’t make contact or bounce
off.
Totally Inelastic: involves greatest loss of
KE. Usu damage done. Most extreme case –
objects stick together.
Which is totally elastic?
Inelastic?
Inelastic Collision
mc = 1000 kg
mt = 3000 kg
vc = 20 m/s
vt = 0
pc =
pt =
m 1v 1 + m 2 v 2
= m1fv1f + m2fv2f
(1000kg)(20m/s) + 0 = (1000)v + (3000)v
(20000 kg m/s) = (1000kg + 3000kg)v
(20000 kg m/s) = (4000 kg)v
(20000 kg m/s) = v
4000 kg
v = 5 m/s
Elastic Collision
mc = 1000 kg
mt = 3000 kg
vc = 20 m/s
vt = 0
Find final velocity of the car if truck has
final velocity of 10 m/s.
m1v1 + m2v2 = m1fv1f + m2fv2f
(1000kg)(20m/s) + 0 =
(1000kg)vc+(3000kg)(10m/s)
20,000 kg m/s = (1000kg)vc+30000 kg m/s
20,000 kg m/s – 30,000 kg m/s = vc
(1000kg)
- 10 m/s = vc
Do Now: On July 4th my family likes to shoot off
fireworks. One rocket was shot straight up, climbed
to a height 18-m and exploded into hundreds of
pieces in all directions at its highest point.
Thinking about conservation laws, think about the
rocket at its highest point just before & just after it
explodes:
How does the rocket’s momentum compare before
& after the explosion?
How does its KE compare compare before & after
the explosion?
Inelastic Collisions
Stick em together
KE “lost” converted
Elastic Collisions – no KE lost.
Bounce off each other.
• Pg 233 #17, 19, 20, recoil prbs24, 25.
• Sentences, equations, show work w/units.
In class
pg 221 #1 write out and hand in to
be graded.
and do pg 219 #1 – 4 calcs
Film Car Crashes or Running with
momentum.
http://www.youtube.com/watch?v=yUpiV2I_IRI