Transcript Momentum

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will earn an extra bonus!
Momentum
The secret of collisions &
explosions
Who Pushes Who
• Rin Tin Tin and the Refrigerator meet at
the 50 yard line
Mass 20 Kg
Mass 160 Kg
Speed 17 m/s
Speed 2 m/s
Who pushes who over the 50 yard line?
Momentum = Mass x Velocity
Whoever has the most momentum = mv
wins
Mass 20 Kg
Mass 160 Kg
Speed 17 m/s
Speed 2 m/s
Momentum = 320 Kg m/s
Momentum = 340 Kg m/s
Momentum = mv
• Mass times velocity!
• Velocity is a vector but here we can
usually think of it as speed
• Example: A speeding car has a mass
of 1000 Kg and a speed of 20 m/s.
What is its momentum?
• mv = 1000kg x 20 m/s = 20,000 kg m/s
Unit of Momentum
Kg m/s
Jump to conservation
Momentum is a Vector
• p = mv
• Force is required to change the momentum of
an object. Newton stated his 2nd law:
SF = Dp/Dt
The rate of change of momentum of a body
equals the net force exerted on it
Equivalent to F = ma
Proof of equivalence of two
forms of Newton’s 2nd Law
SF = Dp/Dt = (mv –mv0)/Dt =
m(v - v0)/ Dt = mDv/Dt = ma
Q: Which form of the law is more
general? (which includes the possibility
that the mass could change?)
Example
• Water leaves a hose at a rate of 1.5
kg/s with speed 20 m/s and hits a car
without splashing back. What force is
exerted by the water on the car?
F = Dp/Dt = (p final - pinitial )/ Dt
= (0 – 30kg m/s)/1sec = -30N
Momentum is Conserved
• The total momentum of an isolated system of
bodies remains the same
• “isolated” means net external force is zero
• Momentum before = momentum after
• m1v1 + m2v2 = m1v1’ + m2v2’
• Applies to all interactions, especially
collisions, explosion-like events, and
“dumpings”
• Closely related to Newton’s 3rd law
Law of Conservation of
Momentum
• Momentum before = momentum after
•
m1v1 + m2v2 = m1v1’ + m2v2’
Apostrophe thingee is pronounced “prime”
Impulse
• Impulse = F Dt = Dp
• Impulse is product of force and time
during which force acts
• Impulse equals change of momentum
• F is usually non uniform and time
interval is usually short
Momentum Lab
• Set target car at the 50 cm mark, with photogate A at the 40 cm mark and
photogate B at the 60 cm mark.
• Place moving car with rubber band onto track with launcher. Pull back as
far as you can and release moving car, record time A and time B on chart.
• Calculate the speed of moving car before collision and speed of target car
after collision.
• Redo trials with 6 different marble combinations. Fill in chart.
• Calulate ∆p to show how how momentum was conserved in each of the
collisions.
Trial
1
2
3
4
5
6
7
Time A
Time B
Sp A
Sp B Mass A
Mass B
Pa
Pb
∆p
Two Kinds of Collision
Courtesy Deer Vally
HS Espace Academy
• Inelastic - sticking
Examples: glue balls fly into each other,air
track gliders with clay
• Elastic – bouncing
• Examples: hard balls or protons collide
Courtesy St.
Mary College
Physics
Department
Dumping Example
Courtesy Easyhaul Cart Inc.
• A 10 kg cart rolls on a frictionless track
at speed v. Suddenly 10 kg of rocks
are dropped straight down into the cart.
What happens to its speed? How
come?
Answer v/2 ; momentum mv is conserved,
m is doubled so v must be halved.
Explain This
• A rock falls to earth. Is momentum
conserved? Include earth in your
explanation
• Does the earth really come up to meet
the rock?
Railroad Cars Collide
Inelastically(stick)
• A 10,000 kg railcar moving 2.4 m/s hits and
sticks with an identical car at rest. What is the
final speed of the two cars?
m1v1
+
m2v2
=
(10,000 kg) (2.4 m/s) + (10,000 kg) (0m/s) =
24,000 kg m/s + 0 kg m/s = (m1 + m2)v’
so v’ = 24,000 kg m/s / 10,000 kg + 10,000 kg
v’ = 24,000 kg m/s /20,000 kg = 1.2 m/s
Elastic Example
• A 3 kg glider moves to the right at 4.0 m/s and
collides elastically with a 1 kg glider moving to
the left at 1.0 m/s. If the first glider moves
back toward the left at 1.0 m/s, how fast does
the second glider move to the right?
Recoil of a pistol (an explosion-like event)
• What is the recoil velocity of a 1 kg pistol that
shoots a .02 kg bullet at 400 m/s?
Initial momentum = 0
& mBvB
+
mpvp =
(0.02kg x 400 m/s) + 1kg x vp =
vp = - 8 m/s Q: Does the shooter recoil too?
Skip Think and Solve # 63 & # 65
New example
• A 3 kg glider moves to the right at 4.0 m/s and
collides inelastically with a 1 kg glider at rest.
What is the final speed of the two joined
together gliders?
m1v1 + m2v2 = (m1 + m2) vf
12 kg m/s + 0 kg m/s = (4kg) (vf)
vf = 3 m/s
Next example
• A 3 kg glider moves to the right at 4.0 m/s and
collides inelastically with a 1 kg glider moving
to the right at 1.0 m/s. What is the final speed
of the two joined together gliders?
m1v1 + m2v2 = (m1 + m2) vf
12 kg m/s + 1kg m/s = 13 kg m/s = (4.0 kg) (vf)
vf = 3.25 m/s
Next example
• A 3 kg glider moves to the right at 4.0 m/s and
collides inelastically with a 1 kg glider moving
to the right at 2.0 m/s. What is the final speed
of the two joined together gliders?
m1v1 + m2v2 = (m1 + m2) vf
12 kg m/s + 1 kg x 2 m/s = 14 kg m/s = 4.0 kg vf
vf = 3.50 m/s
Next example
• A 3 kg glider moves to the right at 4.0 m/s and
collides inelastically with a 1 kg glider moving to
the left at 5.0 m/s. What is the final speed of
the two joined together gliders?
m1v1 + m2v2 = (m1 + m2) vf
12 kg m/s - 1kg x 5 m/s = 7 kg m/s = 4.0 kg vf
vf = 1.75 m/s
Next example
• A 3 kg glider moves to the right at 4.0 m/s and
collides inelastically with a 1 kg glider moving to
the left at 20.0 m/s. What is the final speed of
the two joined together gliders?
m1v1 + m2v2 = (m1 + m2) vf
12 kg m/s - 1kg x 20 m/s = -8 kg m/s = 4.0 kg vf
vf = -2.00 m/s
Sled Collision
• Kids on a sled, total mass 100kg move
to the right at 4.0 m/s. They collide
inelastically with other kids, mass 150
kg, moving to the left at 2.5 m/s. Find
the final velocity of the two sleds.
solution
m1v1
+
m2 v 2
=
(m1+ m2)v’
100Kg x 4m/s –150Kg x 2.5m/s =
400 Kg m/s – 375 Kg m/s
=
25 Kg m/s
=
Vf = 0.1 m/s
250 Kg x Vf
Sled Collision in reverse
• Kids on a sled, total mass 100kg move
to the right at unknown speed v. They
collide inelastically with other kids, mass
150 kg, moving to the left at 2.5 m/s.
The final velocity of the two sleds is 0.2
m/s. Find v
Explosion like Event
• If a stationary student on a skateboard throws
a rock with momentum 10 kg m/s, what
momentum will the student get?
Answer;
-10 kg m/s (Newton’s 3rd Law)
Think and Solve
63)
m 1 v 1 + m 2 v 2 = m1 v 1 ’ + m2 v 2 ’
Let mass of flat car = m
Then mass of diesel engine = 4m
v1 = 5 km/h
v2 = 0
4 m X 5 km/h + 0 = 5 m X Vf
20 m = 5m X Vf
Vf = 4 km/h
65) A) 5 kg X 1 m/s + 0 = 6 kg X Vf
Vf = 5/6 m/s
B) 5 kg X 1 m/s – 1 kg X 4 m/s = 6 kg X Vf
5 kg m/s – 4 kg m/s = 6 kg X Vf
1 kg m/s = 6 kg Vf
Vf = 1/6 m/s
Inelastic
Collision
Lab
To solve for momentum of the system: m1v1 + m2v2= (m1+m2)v
•
• Car 2 is at rest so to solve for v = m1v1/ (m1+m2+mputty)
• Use the rubber band launcher and release the car down the ramp so
it will go at least 60 cm. Place a photogate there, calculate the
velocity of the car at that spot, then using the mass of .060 kg for the
car, calculate its momentum.
• Then, calculate (theoretically) the velocity an inelastic collision
between the original car and another car at the 50 cm mark will
create. Use the following equation to solve for v . v = .06(v1)/.13
• Do the lab as instructed above and calculate the velocity of the
inelastic collision by placing putty on the second car and placing it on
the 50 cm mark, do all the necessary calculations.
• Compare your actual v with your predicted v.
Trial
Mass
One car, no collision
.060 kg
Two cars + putty, inelastic
collision (.06+.06+ .01)
.130 kg
Time A
Speed A
Momentum
“Impulse” Why should you
• Bend your knees when you land?
• Pull back when the baseball enters
your mitt?
• Follow through when you swing?
• Not walk into a punch?
(like Mike Tyson did)
You Predict
• Two gliders of equal mass collide
elastically. The first is moving with
speed v. The second is at rest.
What happens?
First one stops, second moves off at
speed v
But why? Find the answer yourself and get extra credit
Energy Conservation in
Elastic and Inelastic Collisions
• Elastic – kinetic energy is conserved as
well as momentum and total energy
• Inelastic – kinetic energy is not
conserved – some energy turns into
heat
• Elastic – bounce
• Completely inelastic - stick
Ballistic Pendulum
• A bullet of mass m is fired into a block
of wood of mass M suspended from a
string. The bullet remains in the block
which rises a height h. What was the
speed of the bullet? Show that
• v = (2gh)1/2(m + M)/m
or / 2 gh
h
Collisions in Two Dimensions
• Remember momentum p is a vector
• x and y components are conserved
separately
q1
q2
• What is the total vertical momentum?