Download Work, Energy & Power

Work, Energy &
Power
AP Physics 1
What is energy?
• Comes from the Greek, energia, meaning in or at work,
more specifically, it is the ability to do work, or cause
change, a transfer of energy
• Every unit we have or will discuss involves energy, energy
is required to produce a force, torque, velocity, light,
sound, etc. Remember Momentum, an object has energy
based on its movement.
• Energy cannot be created or destroyed, it merely changes
form, also known as the Law of Conservation of Energy
• Conservation of Momentum – Conservation of Energy
E Ne Rgy you ain’t got no alibi
• There are many forms of energy, potential (U or PE),
kinetic (KE), thermal (Eth), elastic potential (SPE),
chemical (Echem),etc. etc. and they are all converted from
one to the other. Thermal is an exception when it comes
to work.
• If we are talking about an isolated system, (nothing
coming in or out) the net change in the total energy would
be 0.
• Any change in energy involves either work and/or heat.
Whhaaaaattt?
• If an object starts from rest and is moved it gains
KE or energy of motion
• If an object is elevated it gains PE or potential
energy.
• A fuel burning releases chemical energy in the form
of heat which causes a gas to expand performing
work on a piston producing kinetic energy
Energy transformations and units
• Energy in Physics is expressed in
JOULES (J)
•
•
•
•
1J=1Nm
4.18 J = 1 calorie
kWh, BTU, calorie, etc
Energy or an change in energycan
be expressed more specifically by
using the term WORK(W)
• Work = F x D
Work = The Scalar Dot Product between Force and Displacement.
So that means if you apply a force on an object and it covers a
displacement you have supplied ENERGY or done WORK on that
object.
Scalar Dot Product?
A product is obviously a result of
multiplying 2 numbers. A scalar is a
quantity with NO DIRECTION.
So basically Work is found by
multiplying the Force times the
displacement and result is
ENERGY, which has no direction
associated with it.
 

W  F  x  Fx cos
A dot product is basically a CONSTRAINT
on the formula. In this case it means that
F and x MUST be parallel. To ensure that
they are parallel we add the cosine on the
end.
Work
The VERTICAL component of the force DOES NOT
cause the block to move the right. The energy imparted to
the box is evident by its motion to the right. Therefore
ONLY the HORIZONTAL COMPONENT of the force
actually creates energy or WORK.
When the FORCE and DISPLACEMENT are in the SAME
DIRECTION you get a POSITIVE WORK VALUE. The
ANGLE between the force and displacement is ZERO
degrees. What happens when you put this in for the
COSINE?
When the FORCE and DISPLACEMENT are in the
OPPOSITE direction, yet still on the same axis, you get a
NEGATIVE WORK VALUE. This negative doesn't mean
the direction!!!! IT simply means that the force and
displacement oppose each other. The ANGLE between the
force and displacement in this case is 180 degrees. What
happens when you put this in for the COSINE?
When the FORCE and DISPLACEMENT are
PERPENDICULAR, you get NO WORK!!! The ANGLE
between the force and displacement in this case is 90
degrees. What happens when you put this in for the
COSINE?
Work
• Work = Fx cos  is the equation for work done at
an angle. Only the component of force parallel with
displacement does work.
• Positive work means energy is added to a system
• Negative work means energy is taken away from a
system
• No displacement = no work, perpendicular forces =
no work
System, schmistem
• Different textbooks, teachers, etc = different
definitions for system
• The thing you are analyzing is always the smallest,
what’s around it is bigger
• Object and System
• System and Environment
• Etc.
The Work Energy Theorem
Up to this point we have learned Kinematics and Newton's Laws. Let 's see what
happens when we apply BOTH to our new formula for WORK!
1. We will start by applying
Newton's second law!
2. Using Kinematic #3!
3. An interesting term
appears called KINETIC
ENERGY or the ENERGY
OF MOTION!
Other Forms
•
•
•
•
•
KE, K = ½ mv2
GPE, PE, Ug = mgh
SPE, Us = ½ kx2, x = distance, k = a spring constant
Krot = ½ Iw2
The kinetic energy of a rolling object is always greater
than non-rolling
• Gravitational potential energy is path independent, height
is all that matters
The Work Energy Theorem
And so what we really have is called the
WORK-ENERGY THEOREM. It
basically means that if we impart
work to an object it will undergo a
CHANGE in speed and thus a
change in KINETIC ENERGY.
Since both WORK and KINETIC
ENERGY are expressed in JOULES,
they are EQUIVALENT TERMS!
" The net WORK done on an object is equal to the change in kinetic
energy of the object."
Example
W=Fxcos
A 70 kg base-runner begins to slide into second base when moving at a
speed of 4.0 m/s. The coefficient of kinetic friction between his
clothes and the earth is 0.70. He slides so that his speed is zero just as
he reaches the base (a) How much energy is lost due to friction acting
on the runner? (b) How far does he slide?
a) W f  K
F f  Fn  mg
W f  0  1 mvo2   1 (70)( 4) 2
2
2
W f  -560 J
 (0.70)(70)(9.8)
= 480.2 N
W f  F f x cos 
 560  (480.2) x(cos 180)
x  1.17 m
An “ugly Prius” does a ¼ mile in 20
seconds.
A Mustang GT does the same in 13.
Do they do the same amount of work?
Technically, yes they exert a force over the same distance, the same
energy, just one is converted at a much faster rate, this is a measure of
power.
Power is the rate at which energy is transformed, or work done per
unit of time
P =E/T = W/T = Fd/t = Fv