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Hewitt/Suchocki/Hewitt
Conceptual Physical Science Fourth
Edition
Chapter 3:
MOMENTUM AND ENERGY
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Momentum: inertia in motion
Momentum
p = momentum (kg*m/s) : m = mass (kg) : v = velocity (m/s)
p = mv
Image from: momentumhockey.com
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Momentum Example
How much momentum does a truck with a mass of
10,000 kg have if it is moving at 10 m/s?
p = m * v = 10,000 * 10 = 100,000kg * m
s
kg*m
s
As you can see from the above example, the units for momentum are:
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Conservation of Momentum
DEFINITION:In the absence of an external force, the momentum of a system
remains unchanged.
Example: Collisions
Net momentumbefore collision= Net momentumaftercollision
Two types of collisions:
1. Elastic CollisionsTwo objects collide, and then bounce off one another.
2. Inelastic CollisionsTwo objects collide, stick together, then continue moving
attached to one another.
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Conservation of Momentum
Elastic Collision:isdefined as a collision whereupon objects collideand then move separately.
(The elastic balls bounce!)
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Elastic Collision Calculation
v = 5 m/sm = 2 kg m = 1 kg
Momentum of blue cart:
pmv
p 2kg 5m
s
p10kg m
s
pmv
p 1kg 0msp0
kgms
Momentum of red cart:
Momentum before collision =
Momentum of blue cart + momentum of red cart = 10+ 0= 10 kgm/s= Momentum after collision
Momentum of blue cart:
pmv
p 2kg 0m
s
p 0kgm
s
10 mv
10 1kg *v
v10 ms
Velocity of red cart:
A cart of 2-kg moving at 5 m/s runs into another 1-kg cart sitting still. If the blue cart comes to a
stop after the collision, what is the velocity of the red cart after the collision?
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Conservation of Momentum
Inelastic Collision:
is defined as a collision whereupon colliding objects
become tangled or coupled together. (Inelastic
collisions are often sticky.)
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Inelastic Collision Calculation
m = 500 kg m = 500 kgv = 10
m/s
A cart of 500 kg moving at 10 m/s runs into another 500 kg cart sitting still. If they lock together,
what is their velocity after the collision?
Momentum of green cart:
pmv
p 500 kg 10m
s
p 5000kgm
s
pmv
p 500 kg 0 msp0
kgms
Momentum of purple cart:
Momentum before collision =
Momentum of green cart + momentum of purple cart = 5000+0= 5000 kgm/s= Momentum after collision
m = 500 kg m = 500 kg
p(m1m2)v final
5000 kg m s 500 kg 500 kg v final5000 kg m s(1000k g)v
final
v final5m
s
Momentum of both carts:
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Work ExampleHow much work needs to be done to accelerate a 500 kg object 3 m/s2to 2 meters?
Step 1: Define what you know.
Step 2: Figure out what you need to solve for.
Step 3: Refer to your equation sheet and decide what
equation to use.
Step 4: Since the problem does not give you force,
we will need to use the equation for force (F=ma)
to ultimately solve for work.
Step 6: Solve.
m = 500 kg
a = 3 m/s2
d = 2 m
W = ?
W = Fd
W = Fd = (ma)d
Step 5: Place the values from Step 1 into the
equation.W = (500 kg)(3 m/s2)(2 m)
W = 3000 J
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Power
Power =Work
time
P =W
t
DEFINITION:
The amount of work done per time ittakes to do it.
UNIT:
Joules/Second = J/S = Watt
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Power
Example: How much power is needed to accelerate a 2000 kg car 5
m/s2a distance of 200 meters in 10 seconds? (Hint: it is a lot!)
PowerWork
time
Power Force* distancetime
P(2000kg)(5
m
s2)(200m)
10s
P2,000,000J
10s200,000
J
s
P200,000W
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Energy
Energy
defined as that which produces changes in matter
Energy cannot be created nor destroyed, only changed in form
Effects of energy observed only when
it is being transferred from one place to another
or it is being transformed from one form to another
Both work and energy are measured in Joules.
!
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(Gravitational) Potential Energy
The upward force when moved at constant velocity is the weight, mg, of the object. Sothe work done in lifting it through height h is:
W = PE = m*g*h
Work done equals Force required to move it upward the vertical distance moved:
W = F*d
DEFINITION:
The amount of gravitational potential energy possessed by an elevated object is equal
to the work done against gravity in raising it.
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(Gravitational) Potential Energy
Equation for gravitational potential energy:PE = weight (W)height (h)
or
PE = mass (m) x gravity (g) x height (h)
Gravitational potential energy examples:
Anything at an elevated height
For an object to get potential energy
someone, or something must do work
to get the object to that elevation.
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(Gravitational) Potential Energy
Example: potential energy of 10-N ball is the same inall 3 cases because work done in elevating it is the same
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(Gravitational) Potential Energy
Example:
How much work do you perform to lift a 25 kg barbell 2
meters? How much potential energy does a 25 kg weight
have when you lifted it?WorkWeight* distance
Work (mg)* height
Work (25kg)(10m
s2)(2m)
Work (250N)(2m)
Work 500J
PE (mg)* h
PE (25kg)(10m
s2)(2m)
PE (250N)(2m)PE 500J
As you can see, the amount of Work you did to lift the barbell is the same as the
amount of gravitational Potential Energy the object has!
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Kinetic Energy
KineticEnergy
is defined as the energy of a moving body
Equation for kinetic energy:
KE = kinetic energy : m = mass : v = velocity
small changes in speedlarge
changesin
KE
Since it is Energy, the units are the same as work andPotential Energy: Joules
KE = m*v2
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ProportionalityThe relative directions variables change.
Exponentially proportional:
KE = m v21
d2Intensity =
Variables are exponentially proportional if one increases as the other increases
(or decreases) by apower of the variable (such as a square).
KE
v
Intensity
d
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Kinetic Energy
Example:
How much Kinetic Energy does a 10 kg object have moving at
10 m/s?
KE 12* mass*speed2
KE1
2(10kg)(10
m
s)2
KE(5kg)(100m2
s
2 )
KE500J
***Show that 2 times the mass results in 2 times the Kinetic Energy while 2 times
the speed results in 4 times the Kinetic Energy!
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Kinetic Energy
How does 2 times the mass result in 2 times the KE but
2 times the velocity is 4 times the KE?
KE1
2 (2*mass)(speed2
)
KE1
2(20kg)(10
m
s)2
KE (10kg)(100m2
s2 )
KE1,000J
KE1
2 (mass)(2*speed)2
KE1
2(10kg)(20
m
s)2
KE (5kg)(400m2
s2)
KE 2,000J
The reason for the difference is that speed has more effect on KE because it is
squared where mass is not!
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Conservation of Energy
Example: energy transforms without net loss or net
gain in the operation of a pile driver
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Conservation of Energy
POTENTIAL ENERGY AT THE TOP =
KINETIC ENERGY AT THE BOTTOM
PEtopKEbottom
(mgh)top(1
2mv 2)bottom
gh
1
2 v2
2ghv2
2ghvbottom
Derivation.