Download Momentum and Energy

Momentum and Energy
Momentum is Mass x Velocity:
Each Plane has Velocity v
Each Plane has Mass m
Each Plane has Momentum  p = mv
Momentum Has Direction
Though they have the same masses and
speeds, their momenta are different.
The Direction of the
Momentum is Vital
By convention, if the momentum
points to the right or up, it is positive.
Similarly, if the momentum points
to the left or down, it is negative.
Impulse Means a Change in
Momentum
Consider a bouncing ball:
pafter = momentum
right after bouncing
Impulse = pafter - pbefore
= F Dt
Note that pbefore < 0 and pafter > 0  F > 0.
pbefore = momentum just
before bouncing
The ball is in contact with the
floor for a period of time Dt.
The force exerted by the floor
causing the ball to bounce is F.
The Impulse-Momentum Theorem
and Newton’s 3rd Law on a
Bouncing Object:
Force of wall
Dp
Fon ball =
on ball:
Dt
Fon ball = -Fon wall; both
forces are applied for the
same period of time, Dt.
Therefore, the changes
in momenta are equal
but opposite.
When Two (or More) Objects Collide,
the Total Momentum, P, is Conserved
v1,before
m1
v1,after
v2,before
m2
Pbefore = m1v1,before + m2v2,before
v2,after
m1
m2
Pafter = m1v1,after + m2v2,after
= m1v1,before + Dp1 + m2v2,before + Dp2
= m1v1,before + Dp1 + m2v2,before - Dp1
= m1v1,before + m2v2,before = Pbefore
If You Exert a Force Over Any
Distance, You Have Done Work
F
F
d
Work = Force × Distance
W=
F
×
d
Work is a form of energy!
There are Different Types of Energy
Mechanical -Energy of Motion
Thermal -Energy of Heat
Nuclear -- Energy
in the Atom
Electromagnetic -Energy of Electricity
Energy is Measured in “Joules”
1 Joule = 1 Newton x 1 meter
= 1 kilogram·meter2/second2
James Prescott Joule, 1818 - 1889
(He showed heat and energy are the
same thing)
Energy is Always Being Transformed
From One Kind to Another
A falling object transforms gravitational
potential energy into
kinetic energy
An explosion may transform chemical energy into
thermal energy
The Total Energy in a Reaction
Remains Constant!
5323 Joules of Energy in
Chemical or
Physical Reaction
5323 Joules of Energy out
(possibly in different forms)
The Work-Energy Theorem:
Although it sounds intimidating, the WorkEnergy Theorem is not a difficult concept.
In short, if you do work on an object, you
change that object’s total energy by exactly
the same amount of work you put into it.
Here, you are pushing the block
Fyou
Fyou
The block keeps moving
vobject
d
Wdone by you = Fyoud
Object’s Change in KE = Fyoud
Kinetic Energy is the Energy
Associated with Motion
Kinetic Energy increases with the mass m that is in motion
Kinetic Energy increases with the speed v of the mass
Kinetic Energy = ½mv2
If I do work W to increase an
object’s kinetic energy, then
KEfinal = KEinitial + W
Another Type of Mechanical
Energy is “Potential” Energy
If this mass m is held
suspended at a height h
then it has gravitational
potential energy. It is
equal to the force due to
gravity, mg, times the
height above the ground:
m
h
GPE = mgh
“Potential Energy” is Like
Having Stored Energy
m
GPE = mgh
If the object starts from
rest, its initial kinetic
energy is zero.
m
As the object falls,
gravitational potential
energy is converted
into kinetic energy,
KE = ½mv2.
Question:
Two people do the same work, but one does it
more quickly than the other. If the work done by
each is the same, what quantity is different?
The Answer is “POWER”
Work Performed
Power =
Time Spent Doing the Work
By this definition, the less time you spend to
perform a certain amount of work, the more
power you exert during that period of time.
Power Has Units of Watts
1 Watt = 1 Joule/second
1 kilowatt·hour
= 1000 watts · 1 hour
= 1000 Joules/sec · 3600 sec
= 3,600,000 Joules
James Watt, 1736 - 1819
Inventor of the Steam Engine
(The kW ·hr is a measure of
energy, NOT of power)