Download Chapter 3 Energy and Conservation Laws

Physics 2001, Professor R. Merry, Keiser College, Nov-Dec 2005
Lecture Notes, Chapter 3, Energy and Conservation Laws
Chapter 3, Energy and Conservation Laws
Physics 2001, Professor Ray Merry
Conservation Laws:
What does it mean for a physical quantity to be conserved?
It means:
The amount of that thing does not change.
E.G. Conservation of mass, means the amount of mass in a system stays constant.
Take the example of a burning cigarette.
Cigarette before burning weighs 10 g.
After burning the butt plus the ash weighs 5
g.
What happened? Is mass conserved?
Burning Cigarette Graphic
What is the Closed System?
Note for all the conservation laws we must include all the parts of the system!
For example, not considering the air in the cigarette example led to an error.
This is the secret to good scientific analysis. What is the total environment or
system?
Linear momentum:
The mass of an object times its velocity.
p = mv Note since v is a vector so is p!
Example, m = 5 kg, v = 10 m/s what is p?
p = 5 x 10 kg m/s = 50 kg m/s
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Physics 2001, Professor R. Merry, Keiser College, Nov-Dec 2005
Lecture Notes, Chapter 3, Energy and Conservation Laws
Note units are kg m/s or mass x velocity. Units.
Newton’s Second Law w Impulse
F= (mv)/t is another way
of stating Newton’s second
law, in terms of
(mv), change in momentum
and
t time for the change to
occur.
We can also state this as
F t = (mv) Where F t is
the impulse of a force.
Impulse Problem
Suppose a ball of .1 kg is in contact with a bat for .2 s, and the force the bat exerts is
5 n. What would the speed of the ball be?
F t = (mv) since original velocity of the ball is 0, (mv) = m x final vel.(vf)
5n x .2s = .1kg x v final
Vf = 1 ns/.1kg = 10 m/s
(n=kg m/s/s nxs = kg m/s n/kg = m/s)
Law of Conservation of Linear Momentum:
The total linear momentum of an isolated system is constant.
Remember this is a vector relationship
If all velocities are in the same direction it is simple, if not we must use vectors to
solve
total mv before = total mv after
1 D Momentum
Problem
A 200kg boy moving at 10 m/s hits 2 50 kg midgets at rest. Both go off together,
but how fast ?
Momentum before = momentum after
Mom.before =200 kg x 10m/s = 2000 kgm/s
Mass after = 50 +50 + 200 = 300 kg
After mom = 300 x V2; 2000 = 300 V2
V2 = 2000/300 = 6.6 m/s
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Physics 2001, Professor R. Merry, Keiser College, Nov-Dec 2005
Lecture Notes, Chapter 3, Energy and Conservation Laws
Work
The force that acts times the distance moved in the direction of the force.
Work = F x d (Joules =Newtons x meters)
Work units are Joules, same as energy.
E.G. Force of 10 N moves 5 m
Wk = 10 N x 5 m = 50 Nm or 50 J
Note- Force is a vector but work is a scalar!
Force vs Work
Note work = force x
distance in direction of
force.
If Force is perpendicular to
motion or displacement
no work is done!
Examples circular motion, moving parallel to floor
Gravitational Work
When we lift a body we do work against gravity,
but when a body falls, gravity does work on it.
If the distances are equal so are the works.
Work = F x d
F = weight = W=mg
Wk=W x d = mgd
Example 10kg falls 5m, what is the work?
Wk = 10kg x 9.8m/s/s x 5m =490J
Energy (E)
The measure of a system's capacity to do work.
That which is transferred when work is done.
Energy is measured in Joules, which are Newtons x meters.
Define kinetic energy:
Kinetic energy (KE) Energy due to motion. Energy that an object has when it is
moving
KE = ½ mv2
Example, 20 kg mass moving at 15 m/s
KE = ½ x 20 kg x (15) 2 =10 x 225 = 2250 J
Potential Energy
Potential energy (PE) is Energy due to an object's position or configuration.
A stretched spring has potential energy.
A raised object has gravitational energy.
Gravitational Potential Energy
Energy due to position, PE
Gravitational PE = mgd
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Physics 2001, Professor R. Merry, Keiser College, Nov-Dec 2005
Lecture Notes, Chapter 3, Energy and Conservation Laws
Other PE’s
elastic potential energy
stretched out rubber band or spring.
internal energy
unburned fuel, battery
PE Problem
We can calculate the potential energy of a given situation if we know the force.
Since work against gravity is weight x height lifted. mgd, PE is the same, mgd.
Wk = m g d. Lift 10 kg, 2 meters
Wk = 10kg x 9.8 m/s/s x 2 m
Wk = 196 J; PE stored = same, 196 J
Work and Potential Energy
Law of conservation of energy:
Energy cannot be created or destroyed, only converted from one form to another.
The total energy in an isolated system is constant.
Eo = Ef (original energy = final energy)
In terms of PE and KE:
PE + KE = constant
Conservation of Energy Problem
A man does a work against gravity of 98 Joules lifting an object.
What is its KE before it strikes if it falls back down?
Energy Conversion and Conservation
Many common devices convert energy from one form to another.
For example your radio converts chemical energy from a battery to electrical to
sound energy.
Although the law of conservation of energy holds, some of the energy ends up in
forms we do not need or want, for example as heat.
Energy Conservation in Society
When we talk about energy conservation in society we mean
Don’t waste energy
Renewable energy is energy that we can recover soon, like wood, or solar energy
Fossil fuels like coal and oil take millions of years to replenish
Elastic collision
Collision in which the total kinetic energy of the colliding objects is the same before
and after the collision.
I.E. KE is conserved.
½ mv2 before = ½ mv2 after
Inelastic collision
Collision in which the total kinetic energy of the colliding bodies after the collision is
not equal to the total kinetic energy before.
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Physics 2001, Professor R. Merry, Keiser College, Nov-Dec 2005
Lecture Notes, Chapter 3, Energy and Conservation Laws
Torque (levers)
Torque is the rotational analog of force.
Torque = force times lever arm
Example teeter totter
Inclined Plane
Inclined plane increases distance moved but decreases force needed.
Power
Power (P): The rate of doing work.
The rate at which energy is transferred or transformed.
Work done divided by the time. Energy transferred divided by the time.
Unit of power is the watt (joule/s)
Power Problem
20 Joules of work is done in 5 s. What is the power?
P = W/t = 20J/5s = 4 watts
Angular momentum
The mass of an object times its speed and times the radius of its path.
mvr
Law of conservation of angular momentum
The total angular momentum of an isolated system is constant.
mvr= constant
Important Equations
Chapter 3 Energy and Conservation Laws
Problems Equation
Comments
Using it
#1,2
Fundamental Equations
p=mv
Linear momentum, p
= mass x vel.
#3,4
F=
Newton’s 2nd law
(mv)/t with impluse. Force
= change in
momentum/time
Wk=
Work done = force x
Fxd
distance moved
#11,12
#15,16
KE = ½
mv2
Kinetic Energy = ½
mass x velocity
squared.
#12,13
PE= W x
d = mgd
Gravitational
Potential Energy =
Problems Equation Comments
Using it
Special Case Equations
#21,22
v=(2gd)1/2 speed after falling
distance d = sq rt
of (2 x acc. of
grav. x d) (v0=0)
2
#27
d= v /2g
Height reached
after given initial
speed v.
mvr =
ang.
mom.
#5
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total mv
before =
total mv
after
angular
momentum= mvR
Mass m, vel. v,
Radius r
Collisions,
conservation of
momentum.
Physics 2001, Professor R. Merry, Keiser College, Nov-Dec 2005
Lecture Notes, Chapter 3, Energy and Conservation Laws
Weight x distance or
mass x g x distance.
#30,31,
Power
Power = work
35
=Wk/t
divided by time.
#21, Conservation of Energy. KE + PE = K: Kinetic Energy plus Potential Energy remain
Constant for an isolated system,
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