Transcript Momentum - TeacherWeb

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
No nickname like “Newton;” maybe it could
have been called an “Isaac.”
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”
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
Two Kinds of Collision(video)
• Inelastic - sticking
Examples: glue balls fly
into each other,air track
gliders with clay
• Elastic – bouncing
• Examples: hard balls or
protons collide
Courtesy
Stephanie
Wong
Courtesy St.
Mary College
Physics
Department
Video Full Screen
New Vocabulary
•
•
•
•
•
Momentum Mass times velocity
Conserved Stays the same
Isolated By itself, net force on it is zero
Elastic collision Objects bounce
Inelastic collision Objects stick
Objects moving toward each
other
• If two carts of equal mass approach
each other with equal speed what is the
total momentum before collision?
Answer: zero
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?
You Predict
• Glider moving with speed v hits glider of
equal mass at rest. They stick. What
will be speed of stuck together gliders
after the collision?
Answer: v/2
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
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 1.0 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 1 m/s = 11 kg m/s = 4.0 kg vf
vf = 2.75 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 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)
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
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
“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)
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
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?