Download Energy and Work notes from class 16-17

What does Hooke’s Law say?
Look Hooke’s Law up on your device or in a
textbook and make notes on it..
Be prepared to share with your neighbor and the
class.
Hooke’s Law Lab
Hooke’s Law relates the amount of force a spring exerts to the amount
of distance a spring stretches.
y = mx
F=kx
Force
Spring
Constant
Stretch
Distance
Hooke’s Law Lab
A spring is said to “obey Hooke’s Law”, or be a “Hooke’s Law
Spring” if the force is directly proportional to the stretching distance.
For an ideal, Hookean spring, the spring stretches a certain distance
for a certain force, regardless of whether the spring is “stretching out”
or “stretching back”.
This is NOT true for a rubber band! A rubber band does NOT obey
Hooke’s law because the rubber band’s stretch depends not only on
force, but whether the rubber band was “stretching out” or “stretching
back”.
After repeated stretching and unstretching, a rubber band loses its
elasticity. An ideal metal spring does not.
Work
What is the symbol for work?
W
Write a word definition for work.
Work = (Component of Force || to Displacement)(Displacement)
Write two formulas for work.
W = F|| x
W = F x cos()
[ = angle between force and displacement]
What are the units for work?
Joules [J]
Work
When is work equal to force times distance?
When the force doing the work on an object is parallel to the
displacement of the object.
When does a force do positive work? Negative work? Zero work?
Positive Work: When the force and the displacement make an acute
angle.
Negative Work: When the force and the displacement make an obtuse
angle.
Zero Work: When the force and the displacement make a
perpendicular angle.
A. Positive
Work
B. Zero
A man carries a box from point A and puts it onto a shelf at point D
C.
Negative
along
the path shown below. In the chart below, put a +, – or 0 to
represent the sign of the work done by the man (WM), the work done
by gravity (Wg), and the net work (Wnet) on the box during each path
segment.
D
Fman
x
B
C
A
Segment AB: Man lifts the box with constant velocity.
Work done by the man’s force
is:
Work done by the gravity is:
Net amount of work done is:
Positive
Negative
Zero
Fgrav
Fnet = 0
A. Positive
Work
B. Zero
A man carries a box from point A and puts it onto a shelf at point D
C.
Negative
along
the path shown below. In the chart below, put a +, – or 0 to
represent the sign of the work done by the man (WM), the work done
by gravity (Wg), and the net work (Wnet) on the box during each path
segment.
x
D
B
Fman
C
A
Segment BC: Man moves with the box with constant velocity.
Work done by the man’s force
is:
Work done by the gravity is:
Net amount of work done is:
Zero
Zero
Zero
Fgrav
Fnet = 0
A. Positive
Work
B. Zero
A man carries a box from point A and puts it onto a shelf at point D
C.
Negative
along
the path shown below. In the chart below, put a +, – or 0 to
represent the sign of the work done by the man (WM), the work done
by gravity (Wg), and the net work (Wnet) on the box during each path
segment.
D
Fman
x
B
C
A
Segment CD: Man raises box at constant speed
to the top of the shelf.
Work done by the man’s force
is:
Work done by the gravity is:
Net amount of work done is:
Positive
Negative
Zero
Fgrav
Fnet = 0
Work Done by a Variable Force
How can the work done by a varying force be calculated? Be specific!
A variable force can be represented by a force vs. displacement graph.
To find work, take the area between the graph and the axis of a force
vs. displacement graph.
Work Done by a Variable Force
Example: A roller coaster car feels a force that varies with its position
on the track as shown in the graph below:
Find the work done when the object is displaced: From x = 0 to x = 5.
Work = 12.5 J
F||
5
0
–5
5
10
15
20
x
A. –50 J
B. –25 J
C. –12.5 J
D. 0 J
E. 12.5 J
F. 25 J
G. 50 J
Work Done by a Variable Force
Find the work done when the object is displaced: From x = 5 to x = 10.
Work = 12.5 J
F||
5
0
–5
5
10
15
20
x
A. –50 J
B. –25 J
C. –12.5 J
D. 0 J
E. 12.5 J
F. 25 J
G. 50 J
Work Done by a Variable Force
Find the work done when the object is displaced: From x = 5 to x = 15.
Work = 0 J
F||
5
0
–5
5
10
15
20
x
A. –50 J
B. –25 J
C. –12.5 J
D. 0 J
E. 12.5 J
F. 25 J
G. 50 J
Work Done by a Variable Force
Find the work done when the object is displaced: From x = 0 to x = 20.
Work = 0 J
F||
5
0
–5
5
10
15
20
x
A. –50 J
B. –25 J
C. –12.5 J
D. 0 J
E. 12.5 J
F. 25 J
G. 50 J
Kinetic Energy, and the Work-Energy Principle
What is kinetic energy?
The form of energy that any moving object has.
What is the symbol for kinetic energy? K
What is the basic equation for kinetic energy?
K = ½mv2
Kinetic Energy, and the Work-Energy Principle
Write the work-energy principle as both a formula and as a sentence.
The net amount of work
done on an object
The sum of all of the
works done by all of the
forces on an object
The work done by the
net force on an object
equals the object’s change in kinetic
energy.
W = K
Kinetic Energy, and the Work-Energy Principle
Combining the Work-Energy Theorem and the Definition of Kinetic
Energy
Wnet
=
Kinetic Energy, and the Work-Energy Principle
Write the work-energy principle as both a formula and as a sentence.
The net amount of work
done on an object
The sum of all of the
works done by all of the
forces on an object
The work done by the
net force on an object
equals the object’s change in kinetic
energy.
W = K
Kinetic Energy, and the Work-Energy Principle
Proof of the work-energy principle:
W net   K
Fnet  x   K
The work energy principle.
Net work is done by the net force.
m a x   K
Net force is mass times acceleration.
v = v + 2aDx
2
2
1
 ax
2 v  v0
2


m v  v0   K
1
2
2
2

2
0

Plug this in to our equation.
Distribute
Kinetic Energy, and the Work-Energy Principle
What is potential energy?
Energy that is “stored” in some form.
What is the symbol for potential energy? U
What is the basic equation for gravitational potential energy?
Ug = mgh
Gravitational potential energy is a property of a two-object system that
includes a planet or a moon.
Potential Energy
Give the spring equation and explain what each symbol represents.
F = –kx
(Force) = (Spring Constant)(Stretch)
Why is there a negative in the spring equation?
To indicate that the direction of the force a spring exerts is opposite to
the direction that the spring is stretched.
We call this a “direction-carrying negative” or a “concept-carrying
negative”. It means that the negative sign is only there to remind us
about direction; we do not use the negative when calculating the
magnitude of the spring’s force!
Potential Energy
What are the units for spring constant?
Newtons/Meters [N/m]
What is the equation for elastic potential energy?
Us = ½kx2
F
kx
x
x
Conservative and Non-Conservative Forces
Explain what a “conservative” force is.
(1) A force that has a potential energy associated with it.
(2) The work done by a C.F. depends only on the start and end
position of the object (being worked on), not the path from start to
finish.
Give two examples of conservative forces.
Force of gravity AND Force of a spring
The work done by gravity/spring is the EXACT SAME as the
potential energy equation for gravity/spring.
Conservative and Non-Conservative Forces
Give an example of a non-conservative force.
FRICTION FRICTION FRICTION FRICTION FRICTION
FRICTION FRICTION FRICTION FRICTION FRICTION
FRICTION FRICTION FRICTION FRICTION FRICTION
FRICTION FRICTION FRICTION FRICTION FRICTION
Give an example of a force that never does any work.
The normal force from a resting surface—it is always perpendicular to
the motion of the object.
Conservative and Non-Conservative Forces
Explain (in general) when potential energy increases and when it
decreases.
Potential energy decreases if the object GOT TO DO WHAT IT
WANTS TO DO!!!!!1111sin(90o)
Potential energy increases if the object WAS FORCED TO DO THE
OPPOSITE OF WHAT IT WANTED TO DO!
Stop
Mechanical Energy and Its Conservation
What is total mechanical energy?
The sum of kinetic and potential energies for an object.
What is a conserved quantity?
A quantity that is neither created nor destroyed.
A quantity that is the same at all times within a closed system.
Mechanical Energy and Its Conservation
Under what circumstances is mechanical energy not conserved?
(1) Mechanical energy is not conserved if there is a non-conservative
force (FRICTION) acting. Friction takes kinetic energy out of the
system and turns it into thermal (heat) energy.
(2) Mechanical energy is not conserved if there is external Work done
on the system. Work done on the system adds energy to the system.
The total mechanical energy initially in a system is equal to the total
mechanical energy at any other time in the system.
IF THESE TWO CONDITIONS ARE MET….
Ki+Ugi+Uei = Kf +Ugf +Uef
Mechanical Energy and Its Conservation
IF THESE TWO CONDITIONS ARE NOT MET….
The more general and more complete form of the equation is…
Ki + Ugi + Uei + Wext =
Kf + Ugf + Uef + Eint
Wext represents work done by forces that are external to the system.
Eint represents internal energy, which is thermal energy from friction.
Energy Conservation with Dissipated Forces
What is a dissipative force?
A force that dissipates (takes away) mechanical energy.
Explain thermal energy.
Thermal energy is the energy an object with a temperature has. It is
caused by the kinetic energies of all of the randomly-moving
molecules in the object.
What is the equation for the work done by (or energy lost to) friction?
Wf = Ffd
(Work done by friction) = (Friction force)(Sliding distance)
Energy Transformations
and the Law of Conservation of Energy
State the law of conservation of energy.
In a closed system, the total energy (sum of all energies of all objects)
remains constant.
Explain what work is in terms of energy.
Work is a change in any type of energy. Work is a transfer of energy
from one object or form to another. Anytime any type of energy
changes, work is done.
Power
What is the symbol for power?
What are the units of power?
P
Watts [W]
What is the basic equation for power (write using words and using
symbols)?
Power = (Work)/(Time)
OR
P = W/t
Give another equation for power
Power = (Force)(Velocity)
P = Fv
Power = (Energy)/(Time)