Download Elastic Collision

Physics 30
Momentum
and
Impulse
UNIT 1
General Outcome:
Students will explain how momentum is conserved when objects
interact in an isolated system.
Specific Outcomes:
 define momentum as a vector quantity equal to the product of the mass and
the velocity of an object
 explain, quantitatively, the concepts of impulse and change in momentum, using
Newton’s laws of motion
 explain, qualitatively, that momentum is conserved in an isolated system
 explain, quantitatively, that momentum is conserved in one-dimensional
interactions in an isolated system
 explain, quantitatively, that momentum is conserved in two-dimensional
interactions in an isolated system
 define, compare and contrast elastic and inelastic collisions, using quantitative
examples, in terms of conservation of kinetic energy
Key Concepts
- impulse
- momentum
- Newton’s laws of motion
- elastic collisions
- inelastic collisions
1
UNIT OUTLINE
Date
Thurs, Feb. 4
Fri, Feb. 5
Concept
Momentum
Reading: pg. 448 - 453
Impulse
Reading: pg. 454 – 467
Mon, Feb. 8
Tues, Feb. 9
Conservation of Linear Momentum
Wed, Feb. 10
Ballistics Pendulum Lab
Thurs, Feb. 11
Fri, Feb. 12
Reading: pg. 468 – 479
Two Dimensional Collisions
Reading: pg. 487 – 495
Assignment
pg. 40 – 43, # 1 – 9, *10
Text:
Pg. 453, # 8, 9, 11, 13 - 16
pg. 44 – 49, # 1 – 15
pg. 51 – 56, # 1 – 10, *11
Lab Report
pg. 58 – 63, # 1 – 3, 5 – 8
Text:
pg. 499, # 5, 6, 8 – 11
pg. 67, # 4
Wed, Feb. 17
Energy in a Collision
Reading: pg. 480 – 486 & pg. 495 – 499
Thurs, Feb. 18
Unit Assignment
Fri, Feb. 19
Quiz
Mon, Feb. 22
Exam
Text:
Pg. 497, PP # 1
pg. 486, # 10 – 11
pg. 499, # 7
Due at the end of class
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MOMENTUM
What You Need to Be Able To Do :
 Define “vector,” “scalar,” “magnitude,” and “time interval”
 Classify momentum, velocity, impulse, force and acceleration as vector quantities
 Classify mass, speed and time as a scalar quantity
 State that momentum is equal to the product of mass times velocity

 Solve for any variable in p  mv

Relate SI units to physics quantities:

o p in Ns or kgm/s;
o m in kg;
o v in m/s or in km/h
Vector quantity:
Scalar quantity:
Momentum:
Equation:
m = mass (kg)

v = velocity (m/s)

p = momentum (kgm/s)
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Eg. 1
a. A student on a skateboard has a combined mass of 70 kg. Calculate the
momentum of the student-skateboard system if he is travelling west at
1.2 m/s.
b. An athlete on a sled in the Winter Olympics skeleton event has a
velocity of 35 m/s [N]. If the momentum of the athlete-sled system
has a magnitude of 2.73 x 103 kg·m/s, what is the combined mass of the
athlete and sled?
c. A 3.5 kg Canada goose has a momentum of magnitude 49 kg·m/s while
flying 36 N of E. What is the velocity of the goose?
Your turn: pgg. 451, PP # 1a, 2
4
Eg. 2 A hockey puck has a momentum of magnitude 63.7 kg·m/s while moving
down the ice at 18.5 S of W. What are the horizontal and vertical components
of the puck’s momentum?
Eg. 3 An object has a momentum of 3.64 x 103 kgm/s [E]. Determine the
momentum of the object if the mass increases to twice its original value and a
decrease in the applied force causes the speed to become ¼ its original value.
The direction of the velocity remains the same.
Your turn: pg. 452, PP # 1, 2
5
Newton’s Second Law:
Eg. 4 Determine the change in momentum of a 2.4 kg cart that accelerates
from 3.0 m/s [right] to 5.0 m/s [right].
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IMPULSE
What You Need To Be Able To Do:
 Classify impulse, force and acceleration as vector quantities
 Relate SI units to physics quantities:
o impulse in NS or in kgm/s;









o F in N or in kgm/s2 or in J/m;
o a in m/s2;
o t and t in s, or in h, or in min., or in a
State that the impulse of an object is equal to the change in its momentum
Use delta notation appropriately
Solve for the magnitude of any variable in:
impulse =  p , impulse = m v , impulse = Fnet t
State that the area under a Fnet vs. t graph is equal to the impulse
Calculate simple areas
SE Calculate complex areas
SE Show an understanding of what positive area and negative area mean
SE Derive formulas for impulse from Newton’s third law ( FAB  FBA ) and Newton’s second
law ( F  ma ) and kinematics formulas for acceleration
Impulse:
Equation:
Fnet = net Force (N)
t = change in time (s)
m = mass (kg)

v = change in velocity (m/s)
Units:
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Eg. 1 Find the impulse in each situation:
a. An object undergoes a change in its momentum, from 3.55 kgm/s [west] to
8.37 kgm/s [west].
b. An average net force of 18.5 N acts east on an object for 9.6 x 10-2 s.
c. A 1.75 kg object accelerates from 9.50 m/s [south] to 2.50 m/s [north].
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Eg. 2 A 75 kg man is involved in a car accident. He was initially traveling at
65 km/h when he hit a large truck. Determine how much force would be
exerted on his body if
a) he had no airbag in his car and he came to rest against the steering
wheel in 1/30 s.
b) he did have an airbag that inflated and deflated correctly, bringing him
to a rest over a time of 100 ms.
In any situation, impulse remains constant – the value does not change. What
CAN be changed is the magnitude of the net force and the time the force is
applied:
FORCE HURTS!
To minimize damage, need to minimize Fnet, which means maximizing t.
i.e. A cushioned surface reduces the net force by increasing the amount of
time the force is applied.
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Eg. 3 A 56.7 g tennis ball is travelling west at 22.5 m/s when it is struck by a
racket moving east. The racket applies a net force of 225 N to the ball. If the
racket is in contact with the ball for 25.0 ms
a. what is the final velocity of the ball?
b. what is the impulse on the ball provided by the racket?
c. what is the impulse on the racket provided by the ball?
Your turn: pg. 458, PP # 1, 2
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Eg. 4 As shown in the graph below, a 2.50 kg object is acted on by a force
[south].
If the object had a final velocity of 3.73 m/s [south] at 0.86 s, what was its
initial velocity?
Your turn: pg. 467, # 7
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CONSERVATION OF LINEAR MOMENTUM
What You Need To Be Able To Do:
 Define “isolated system”
 Define “conserved”
 State that momentum is conserved in an isolated system
 Calculate any variable in a linear conservation of momentum situation:
o Hit and bounce
o Hit and stick
o Explosion
 Draw vector addition diagrams for linear interactions
 SE Predict whether or not momentum will be conserved given a description of a system
System –
Closed system –
Isolated system –
Collision –
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Investigation – OBSERVING COLLINEAR COLLISIONS
Perform the following bounce apart collisions and record your observations.
TRIAL 1, 2, 3
Red Car
Blue Car
Mass
1 bar
1 bar
Velocity Before
1 right
stationary
1 left
2 left
Velocity After
TRIAL 4, 5, 6
Red Car
Blue Car
Mass
1 bar
2 bars
Velocity Before
1 right
stationary
1 left
2 left
Velocity After
TRIAL 7
Red Car
Blue Car
Mass
2 bars
1 bar
Velocity Before
1 right
stationary
Red Car
Blue Car
Mass
2 bars
2 bars
Velocity Before
1 right
stationary
Velocity After
TRIAL 8
Velocity After
Perform the following explosion collisions and record your observations.
TRIAL 7
Red Car
Blue Car
Mass
1 bar
1 bar
Velocity Before
stationary
stationary
Red Car
Blue Car
Mass
1 bar
2 bars
Velocity Before
stationary
stationary
Velocity After
TRIAL 8
Velocity After
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Perform the following collide and stick collisions and record your observations.
TRIAL 9, 10, 11
Red Car
Blue Car
Mass
1 bar
1 bar
Velocity Before
1 right
stationary
1 left
2 left
Velocity After
TRIAL 12, 13, 14
Red Car
Blue Car
Mass
1 bar
2 bars
Velocity Before
1 right
stationary
1 left
2 left
Velocity After
TRIAL 15, 16, 17
Red Car
Blue Car
Mass
2 bars
1 bar
Velocity Before
1 right
stationary
1 left
2 left
Velocity After
TRIAL 18, 19, 20
Red Car
Blue Car
Mass
2 bars
1 bar
Velocity Before
2 right
stationary
1 left
2 left
Velocity After
Law of Conservation of Momentum –
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Collide and Stick:
Eg. 1 A 2000 kg truck moving 12.0 m/s west collides with a stationary 1500 kg
car. If they lock together after impact, what is their common velocity?
Eg. 2 A 40.0 g object moving with a velocity of 9.00 m/s to the right collides
with a 55.0 g object moving with a velocity of 6.00 m/s left. If the two objects
stick together upon collision, what is the velocity of the combined masses after
the collision?
Your turn: pg. 477, PP # 1, 2
15
Eg. 3 A rifle with a mass of 2.40 kg fires a bullet with a speed of 800 m/s. The
rifle recoils at 4.75 m/s. What is the bullet’s mass?
Your turn: pg. 476, PP # 1
Eg. 3 A 100 g ball moving at a constant velocity of 200 cm/s strikes a 400 g ball
that is at rest. After the collision, the first ball rebounds straight back at 120
cm/s. Calculate the final velocity of the second ball.
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Eg. 4 A 1.50 kg ball moving 6.0 m/s right collides with a 2.00 kg ball travelling
12.0 m/s left. After collision the first ball bounces left at 8.0 m/s.
a. Find the resulting velocity of the second ball.
b. Find the impulse imparted to the second ball from the first ball.
Your turn: pg. 479, # 1, 2
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COLLISIONS IN TWO DIMENSIONS
What You Need To Be Able To Do:
 Define perpendicular components
 Draw vector addition diagrams for 2-D interactions
 Calculate one speed in a 2-D conservation of momentum 90 situation
 Calculate one rectilinear component or the resultant given one or more sides and/or angle
 SE Analyze 2-D interactions:
o Two objects moving towards each other at 90, and hit and stick
o One object scattering off a stationary object with the angle between the paths after
the collision being 90 (SE other than 90)
o Two objects moving towards each other at an angle other than 90, and hit and stick
or hit and bounce (SE)
o Explosions with three objects (SE)
Law of Conservation of Momentum (in two dimensions) –
18
Eg. 1 A 4.0 kg object is traveling south at a velocity of 2.8 m/s when it collides
with a 6.0 kg object traveling east at a velocity of 3.0 m/s. If these two
objects stick together upon collision, at what velocity does the centre of mass
move?
Your turn: pg. 492, PP # 1, 2
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Eg. 2 A 2600 kg SUV traveling 10.0 m/s east collides with a stationary 1200 kg
car. After the collision the SUV ends up moving 6.00 m/s, 50.0 N of E. Find
the resulting velocity of the car.
Your turn: pg. 491, PP # 1
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Eg. 3 A 120 g firecracker blows into three equal pieces:
A: velocity = 20.0 m/s east
B: velocity = 12.0 m/s on a bearing of 240
C: find the resulting speed of the third piece
Your turn: pg. 494, PP # 1; pg. 491, P # 2; pg. 494, PP # 2
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ENERGY IN A COLLISION
What You Need To Be Able To Do:
 Classify energy as scalar
 Define “elastic collision,” “inelastic collision”







Calculate Ek  1 mv 2
2
Calculate Ek initial, Ek final for up to two moving objects
Use Ek values to classify collisions: Eki = Ekf means elastic
Eki > Ekf means inelastic
Relate SI units to physics quantities:
o E in J or in kgm2/s2 or in Nm
SE Solve for any variable using the concept that in an elastic collision, Eki = Ekf
SE Explain what has happened in terms of the work done by non-conservative forces to
the Eki in an inelastic collision
SE Compare and contrast the conservation of momentum and kinetic energy during any
collision
In all collisions:
- momentum of the system is conserved
- total energy of the system is conserved
- kinetic energy of the system may or may not be conserved:
Elastic Collision –
Inelastic Collision –
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Eg. 1 A 1200 kg car traveling at a velocity of 10.0 m/s east on an icy road
collides with a 1500 kg stationary truck.
a. Determine the resulting speed if they interlock?
b. Compare the kinetic energy of the vehicles before and after the
collision.
Your turn: pg. 482, PP # 1, 2
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Eg. 2 A truck of mass 3000 kg, moving at 5.0 m/s on a level, icy road, bumps
into the rear of a car moving at 2.0 m/s in the same direction. After the impact
the truck has a velocity of 3.0 m/s and the car a velocity of 6.0 m/s, both
forward.
a. What is the mass of the car?
b. Was the collision elastic?
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Eg. 3 In an isolated system, a 50.0 kg object is moving east at an unknown
velocity when it collides with a 60.0 kg stationary object. After the collision,
the 50.0 kg object is travelling at a velocity of 6.0 m/s [50.0 N of E] and the
60.0 kg object is travelling at a velocity of 6.3 m/s [38.0 S of E].
a. What was the velocity of the 50.0 kg object before the collision?
b. Is this an elastic or inelastic collision?
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FORMULAE
Momentum:

p  mv
Impulse:
𝐹⃗𝑛𝑒𝑡 ∆𝑡 = 𝑚∆𝑣⃗
impulse = p
impulse = m v
impulse = Fnet t
Conservation of Momentum (Physics Principle # 4):
𝑝⃗𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑝⃗𝑎𝑓𝑡𝑒𝑟
Type of Collision
Linear
Bounce Apart
𝑚1 𝑣⃗1 + 𝑚2 𝑣⃗2 = 𝑚1 𝑣⃗1 ′ + 𝑚2 𝑣⃗2 ′
Collide & Stick
𝑚1 𝑣⃗1 + 𝑚2 𝑣⃗2 = 𝑚12 𝑣⃗12 ′
Explosion
𝑚12 𝑣⃗12 = 𝑚1 𝑣⃗1′ + 𝑚2 𝑣⃗2′
Type of Collision
Bounce Apart
Collide & Stick
Explosion
Two-Dimensional
𝑚1 𝑣⃗1𝑥 + 𝑚2 𝑣⃗2𝑥 = 𝑚1 𝑣⃗1𝑥 ′ + 𝑚2 𝑣⃗2𝑥 ′
𝑚1 𝑣⃗1𝑦 + 𝑚2 𝑣⃗2𝑦 = 𝑚1 𝑣⃗1𝑦 ′ + 𝑚2 𝑣⃗2𝑦 ′
𝑚1 𝑣⃗1𝑥 + 𝑚2 𝑣⃗2𝑥 = 𝑚12 𝑣⃗12𝑥 ′
𝑚1 𝑣⃗1𝑦 + 𝑚2 𝑣⃗2𝑦 = 𝑚12 𝑣⃗12𝑦 ′
′
𝑚123 𝑣⃗123 = 𝑚1 𝑣⃗1′ + 𝑚2 𝑣⃗2′ + 𝑚3 𝑣⃗3𝑦
′
′
′
𝑚123 𝑣⃗123𝑦 = 𝑚1 𝑣⃗1𝑦
+ 𝑚2 𝑣⃗2𝑦
+ 𝑚3 𝑣⃗3𝑦
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