1. The Currency of the Universe
Energy
The Currency of the Universe
Standards:
2a Students will be able to calculate the kinetic energy of an object using KE=1/2 mv2.
2b Students will be able to calculate the gravitational potential energy of an object using the equation PE=mg delta h where delta h is the change in elevation.
2h* Students will be able to solve conservation of energy problems with springs and capacitors.
NGSS
HS-PS3-1 Create a computational model to calculate the change of energy of one component in a system when the change of another component and energy flows into and out of the system are known.
HS-PS3-3 Design, build and refine a device that works within given constraints to convert one form of energy into another.
This is a good direct lecture hitting the major points of energy that can be done during a late start schedule. Has useful examples in check questions and discusses there being one energy but many expressions of this energy. Revised in 2016

2. Energy in General
Energy is a quantity that can cause change in a body or system.
Energy is a scalar quantity measured in Joules=N m = kg m2/s2
Energy is expressed in different forms and can be transformed from one form to another without loss.
Energy is conserved for a single body or system when there are no outside forces
Question: Define energy. Is energy a scalar or vector quantity? What units are used to measure energy? What is unique about transformations from one form of energy to another? When is energy conserved?
Activities:
Quickly run through these generalities about energy… it’s the quantity that causes change in objects and systems, it’s a scalar measured in Joules.
Talk about how there is one energy but many different expressions of energy. There’s energy expressed motion of an object, in the temperature of an object, there is stored energy something has because it is in a gravitational, electric or magnetic field, there is energy stored due to nuclear forces and expressed as mass itself. There is one energy but many ways to experience it.
Discuss that energy can change how it is expressed w/o loss. That is the energy expressed as motion can compress a spring and become the energy stored in a spring which can then be released and propel a ball so the energy is then stored in a gravitational field and so forth. All this is done without using up the energy.
Discuss how energy is a conserved quantity. Specifically it is conserved when there are no outside forces. This is similar to momentum and means energy is always conserved if you make your system big enough. But energy is also conserved not only for a system of objects (like momentum), but also for single objects.

3. Mechanical Energy
Energy Expression
Definition
Equation
Kinetic Energy
Energy expressed in motion of an object
KE = ½ mv2
Gravitational Potential Energy
Energy stored due to an object’s position in a gravitational field
PEg =mg Dh
Elastic Potential Energy
Energy stored in the stretch or squashing of a spring or other type of elastic object
PEe = ½ k Dx2
Questions: List the three expressions of energy that are considered mechanical energy. Define each and state the equation used to find their magnitudes. When is mechanical energy conserved?
Activities:
Write definition on board and then add names.
Then give equations and discuss doubling one variable and what it does to others. Include doublling velocity, elevation and displacement. Also ½ mass, spring constant, and displacement.
Point out that Gravitational PE equation is only for near Earth’s surface and really is weight x elevation change.
State that sum of these three expressions of energy is called mechanical energy and that it is conserved for single objects and systems of objects when there is no force and even when there is an outside force as long as its gravity, elastic force or other conservative force.
Mechanical energy is conserved when there are no outside forces or when the only outside forces are due to gravitational or elastic forces.

4. Mechanical Energy (ME)
Kinetic energy (KE) is the energy due to an object’s motion =1/2 mv2
Gravitational Potential Energy = the energy stored in the magnetic field between Earth and another body =mg Dh
Elastic potential energy = energy stored by stretching spring or other elastic object = ½ k Dx2
ME conserved for object or system when there are no outside forces or when the outside forces are gravity, a spring or some other conservative force.
Question: Make a chart listing the different forms of mechanical energy and the equations used to calculate their magnitudes. When is mechanical energy conserved?

5. Check question
Each of the balls to right has a speed of 1 m/s and a mass of 2 kg. The directions of their velocities are indicated by the arrows. What is the total kinetic energy of the system of balls?

6. Check Questions: Some Energy Math
A car traveling at 40 mph has a certain kinetic energy. How much more KE does it have when it travels at 80 mph?
A firefighter has a certain gravitational PE when he climbs half way up a ladder. How much more PE will he have when he is at the top of the ladder?
An elastic ball stores a certain amount of PE when it is compressed 1 mm. How much more PE will it store when it is compressed 2 mm?

7. Work (W)
Work is a force that changes the energy of a body or system. Scalar w/ same units as energy.
Work = force x distance object moves in direction of force = Fd (cos q)
Work is positive if force is in direction of motion and increases energy.
Work is negative if force is in opposite direction of motion and decreases energy.
Force and force components perpendicular to motion DO NO WORK
Question: What is mechanical work? Is it a scalar or vector quantity and what units are used to measure it? How is work related to the mechanical energy of a body or system? When is work considered positive and when is it considered negative? How much work does a force or force component which is perpendicular to an object’s motion do on the object? Write an equation summarizing the relationship between work and mechanical energy.
Activities:
Refer to an outside force causing a change in velocity, outside force x time (impulse) causing a change in momentum. Similarly an outside force x distance is called a work and causes a change in energy.
Briefly define work as a force that transfers energy into a system or object. State that work is measured in the same units as energy because it is a change in energy and work is a scalar because it is a change in energy.
Write equation for work on board and discuss how distance and force only do work if in same or opposite directions. Give example of force acting in direction object is moving, force acting opposite direction object moving and force acting perdicular to the direction object is moving as cases where energy increases, decreases in does not change resulting in positive work, negative work and no work being done. For physics E introduce the cos theta term as a mathematical way to quantify this.
Finish off with statement once again that work transfers energy into a body or system.

8. Work and Energy Relationships
Mechanical Energy
Kinetic Energy
Elastic Potential Energy
Gravitational Potential Energy
Positive Work
Negative Work
Activities
Show above picture and derive the energy equation.
Go through money analogy with checking account, savings account and treasury bonds standing in for kinetic energy, gravitational potential energy and elastic potential energy.
Analogize positive work as deposits which increase your wealth and negative work as debits that deduct from your wealth. Write wealth equation.
Write the wealth equation and compare it to the Energy equation. Discuss how like the many money accounts there are many energy accounts, Money can be moved from one account to another w/o loss like energy can move between kinetic, PE g and PE e accounts w/o loss. There is one kind of money just like there is one type of energy but how it is expressed can be different.
Discuss how will add another energy transfer method and energy account when talk about thermal energy.
Discuss how book only gives first term in its work-energy equation and why this is incomplete. Write full kinetic energy-work equation and discuss how it is useful when dealing with a force that is constant over a distance.
W=DKE + DPEg + DPEE

9. Check Question
Mr. DeVoe lifts up a trash can and moves it to the curb every Thursday night. State whether work is done by Mr. DeVoe’s lifting force and if the work is positive or negative.
Picking can up
Moving can horizontally at constant speed
Slowing can down
Lowering can

10. Power (P) Power is the rate at which energy is used.
If machine A has twice the power of machine B, it can get the same amount of work done in half the time or twice the amount of work done in the same time.
Power = Work / time for work to be done = W/t
Scalar quantity with units of Joules/ second =Watt
Question: Define power. Explain what a more powerful machine can do vs. a less powerful one. Is power a scalar or vector quantity and what units are used to measure it? Write the mathematical relationship between power, work and time.

11. Check Question
A 400 N student climbs a flight of stairs that is 10 m tall. The student does this climb in 10 seconds.
How much work does the student do during this climb?
What type of energy does the work change?
What is the power of the student?

12. Expressions of Mechanical Energy
Kinetic Energy = the energy expressed as an object’s motion (KE = ½ mv2)
Doubling the speed means…
Gravitational Potential Energy= Energy stored due to an object’s height above a reference level. (PE gravitational = mg Dh)
Elastic or Spring Potential Energy= Energy stored in the stretch or compression of an elastic object (PE elastic=1/2 k Dx2)
Internal energy (U) is NOT mechanical energy
Make a chart listing the three expressions of mechanical energy, their definitions and the equations used to calculate their magnitudes. What type of energy is not considered mechanical?

13. Mechanical Work
Work is done when an outside force changes the energy of an object or system.
Work = force x distance object moves in direction of force.
W=Fd cos q
No work done if no motion or force is perpendicular to motion
Work has same units and is scalar like energy
Work on vs. Work by, + vs. - work
Questions: How is work related to mechanical energy? What units are used to measure work? Is work a scalar or vector quantity? Write the equation used to calculate work. How much work is done by a force that causes no motion of an object? How much work is done by a force that is perpendicular to the motion of an object? Distinguish between work on and by an object? Which produces positive and which produces negative work?
Activities:
Start with toy truck and discuss how outside force can change the speed, elevation or shape of truck. Discuss how if force in same direction as motion, velocity increases. If in opposite direction, velocity decreases and if perpendicular the direction of truck changes but speed stays same. We say the force did work on the truck for the first two. Define work as force that causes change in energy of truck.
Write mathematical equation of work (W=Fd) and emphasize that force must at least be partially in same or opposite direction of motion. Add cos theta to assure that this is true for physics E. Show that units are same as energy and this is also a scalar quantity.
Talk about bowling around the earth and how much track you would need. Point out both gravity and normal force are perpendicular to motion so they do NO work…bowling ball doesn’t speed up or slow down because of these forces.
Briefly discuss work on an object as energy flowing into the object and work by as energy moving out of an object. First is a positive work, second is a negative work.

14. Work-Energy Theorem Work-kinetic energy theorem
Work = change in kinetic energy
True if no change in height or elastic displacement
Work-mechanical energy theorem
Work= DKE +D PE g +D PE e
True if no change in temperature
First law of Thermodynamics
Work + Heat Flow = DKE +D PE g +D PE e + DU
Always true
Questions: Write the work-kinetic energy, work mechanical energy and first law of thermodynamics equations. When is each true?
Activities:
1) Construct Venn diagram of 1) kinetic energy and work and write equation 2) Add PE e and PE g and write equation 3) add U and Q and write equation. State when each true.

15. Mechanical Energy
Mechanical Energy is the ability to cause changes in velocity, elevation or how much an elastic material is compressed or stretched.
Scalar quantity w/ units of = Joules = Nm= kg m2/s2
Mechanical energy can switch from one form to another w/o loss
Conserved for single objects when there are no outside forces or when the only outside forces are gravity and elastic forces.
Not conserved when friction or air resistance act
Questions: Define mechanical energy. What type of changes can it cause in a body? What units is it measured in and is it a vector or scalar? Is there only one way for energy to manifest itself? When is mechanical energy conserved for a single object? When is it not?
Activities:
Hold ball above ground and discuss how it has the ability to change the motion, position or shape of another object. We say the ball has mechanical energy. Define mechanical energy as ability to cause changes in velocity, elevation or shape.
Mechanical energy is a scalar quantity measured in joules= newton-meter = kg m2/s2. Scalar quantity means direction doesn’t matter and that you do not need to break up energy into perpendicular components.
State that energy is conserved quantity when no force or when only forces acting are elastic or gravity. Not conserved when friction, air resistance or other non-conservative force act.

16. Power
Rate at which work is done or changed into another form of energy
Power = work / time
Units of watts or Joules / second, scalar quantity
More powerful machine
Gets same work done in less time
Gets more work done in same time
Define power, what are its units and is it a vector or scalar quantity? Write the equation for power.