Unit 7 – Work & Energy

Lesson 1: Work & Kinetic Energy & PowerLesson 2: Gravitational Potential Energy & Conservation of

Mechanical EnergyLesson 3: Elastic Potential Energy (optional)

Lesson 4: Mechanical Energy NOT Conserved

Lesson 1: Work & Kinetic Energy

Demos: skidding

WorkWhat is the variable for Work?

What is the equation for Work when the Force is constant. (The equation that includes θ, but not )

What is the unit for Work, and based on the equation for Work, what units make this up?

WorkWhen is Work done (according to physics)?

When is Work NOT done (W=0) even when a Force acts on an object?

WorkWhat would cause more Work to be done in a certain situation compared to another situation? (address all 3 variables) In other words, according to the equation, what would cause there to be an increase in the Work?

WorkWhen is Work positive?

When is Work negative?

Is Work a vector or a scalar?

WorkHow do you find the total or net Work (Wnet) done by all the forces on an object?

Energy What is the physics definition of energy?

What is the unit for any kind of energy?

How does this compare to the unit of Work?

Kinetic EnergyWhat is Kinetic Energy?

What is the equation for Kinetic Energy?

What would cause an object to have more KE than another object?

What is the unit for Kinetic Energy?

Is KE a vector or a scalar? (Does it have direction or not?)

Work – Energy TheoremWhat is the Work-Energy Theorem?

What would cause the net Work on an object to increase based upon the Work-Energy Theorem?

Work – Energy TheoremWhat would cause the net Work to be positive based upon the Work-Energy Theorem?

What would cause the net Work to be negativebased upon the Work-Energy Theorem?

PowerWhat is the physics definition of Power?

What is the variable for Power?What is the equation for Power?

PowerWhat is the unit for Power?

What units make up the unit for Power? (look at the equation)

How many Watts make 1 Horsepower?

WorkYou are now walking down the hall at a constant velocity while holding the book in the elevated position. What can be said about the Work that you are doing on the book?A. PositiveB. NegativeC. Work is done, but whether it is positive or

negative can’t be determinedD. No Work is doneE. None of these can be determined

WorkWhen you are moving your huge entertainment center starts sliding down the ramp! You jump in and try to stop it by pushing on it before it hits the ground. While it is still sliding (there is friction), how many forces are doing work on the box?A. No forcesB. 1 forceC. 2 forcesD. 3 forcesE. 4 forcesF. Can’t be determined

WorkWhen you are moving your huge entertainment center starts sliding down the ramp! You jump in and try to stop it by pushing on it before it hits the ground. While it is still sliding (there is friction), how many forces are doing negative work on the box?A. no forcesB. 1 forceC. 2 forcesD. 3 forcesE. Can’t be determined

WorkWhen you are moving your huge entertainment center starts sliding down the ramp! You jump in and try to stop it by pushing on it before it hits the ground. While it is still sliding (there is friction), how many forces are doing positive work on the box?A. no forcesB. 1 forceC. 2 forcesD. 3 forcesE. Can’t be determined

Work

Does Work have direction?A. YesB. NoC. Sometimes

You are pulling a 50kg box by a rope at 40° with 600N across a floor that has 200N of friction for 20m.

How much Work is the Force of Tension doing on the box?A. 12000 JB. 9192 JC. 5192 JD. 0 JE. None of these

You are pulling a 50kg box by a rope at 40° with 600N across a floor that has 200N of friction for 20m.

How much Work is friction doing on the box?A. 4000 JB. – 4000 JC. 3064 JD. – 3064 JE. None of these

You are pulling a 50kg box by a rope at 40° with 600N across a floor that has 200N of friction for 20m.

How much Work does Fg do on the box?A. 9800 JB. 7507 JC. 1000 JD. 0 JE. None of these

You are pulling a 50kg box by a rope at 40° with 600N across a floor that has 200N of friction for 20m.

What is the net (total) Work done on the box?A. 5193 JB. 8000 JC. 13193 JD. 16000 JE. None of these

You are pulling a 50kg box by a rope at 40° with 600N across a floor that has 200N of friction for 20m.

How fast will the box be going after 20m if it started from rest?A. 14.4 m/sB. 19.2 m/sC. 21.9 m/sD. None of theseE. Can’t be determined

You are pulling 100kg crate by a rope at 40° with for 15m. What is the net Work done on the box if it was initially sliding at 1m/s and ended up with a speed of 3m/s?

A. 200 JB. 150 JC. 10 JD. None of theseE. Can’t be determined

You are pulling 100kg crate by a rope at 40° with for 15m. What is the Work done by Tension on the box if it was initially sliding at 1m/s and ended up with a speed of 3m/s?

A. 153 JB. 150 JC. 115 JD. None of theseE. Can’t be determined

You are pulling 100kg crate by a rope at 40° with for 15m. What would cause the net Work done on the box to be negative if it was initially sliding at 1m/s?

A. If friction was greater than TensionB. If the crate slowed downC. Both of theseD. Neither of theseE. Net Work can’t be negative b/c it doesn’t

have direction

WorkA truck is initially driving North at 60pmh. After some time the truck is now driving South at 60mph. During this process: 1) has unbalanced Forces (ΣF≠0) acted on the truck; 2) has there been net Work (Wnet ≠0) done on the truck?A. Yes; YesB. Yes; NoC. No; YesD. No; NoE. Can’t be determined

WorkA ball is swung in a vertical circle such that the string always remains taut. The only forces acting on the ball are gravity and Tension. Which of the following is true about the given quantities as the ball goes from the top of the circle to the bottom?

ΔKE WFg WFTWnet

A. + + + +B. + + 0 +C. + – 0 +D. – – 0 –E. – + – –

You riding your bike at a certain speed and skid on your drive-way to a stop. If you were going twice as fast, how much more distance will you skid until you come to a stop?A. The sameB. 1.5x as farC. 2x as farD. 3x as farE. 4x as far

PowerArnold pushes a box at a constant speed of 4m/s for 40m. Palmer pushes an identical box at the same speed for 80m. Which demonstrated more Power?A. ArnoldB. PalmerC. Both the sameD. Can’t be determined

Power

Bubba could lift a 50kg crate of shrimp 2m in 0.25s. How much Power did he demonstrate?A. 6.25 WattsB. 25 WattsC. 100 WattsD. 400 WattsE. None of these

Momentum vs WorkMomentum-Impulse Work-Energy

Theorem Theorem

Lesson 2 – Gravitational Potential Energy & Conservation of Mechanical Energy

Demos: 4 colored tracks, pendulum

Gravitational Potential Energy (PEg)What is the equation for gravitational potential energy (PEg)?

What is the unit for PEg ?

Gravitational Potential Energy (PEg)When does an object have PEg ?

When does an object NOT have PEg ?

What would cause an object to have more PEg than another object?

Mechanical Energy (ME)What is the physics definition of Mechanical Energy (ME)?

What is the equation for ME?

Conservation of Mechanical EnergyWhen is Mechanical Energy conserved?

What does it mean to say that Mechanical Energy is conserved?

Conservation of Mechanical EnergyWhat is a conservative force?

Conservation of EnergyWhat does the Law of Conservation of Energy state? (same one from elementary school)

Is the Energy in this law the same as Mechanical Energy, or is Mechanical Energy just a type of energy that is only a part of the Energy that is refer to in this law?

Gravitational Potential Energy (PEg)A 2kg book rests flat in the middle of a 1.5m tall table on the 2nd story of a house (5m above the ground). How much Gravitational Potential Energy (PEg) does it have at this point?A. 0 JB. 24.4 JC. 98 JD. Any of theseE. None of these

What did you learn?

Where did mgh come from?

Conservation of Mechanical EnergyMechanical Energy is conserved when only conservative forces act on an object, or nonconservative forces at perpendicular to the object’s motion.

Conservative Forces Nonconservative Forces

Conservation of Mech Energy?A sled slides up an iced embankment until it momentary stops at the highest point (ignore friction). Is mechanical energy conserved?A. YesB. NoC. Can’t be determined

Conservation of Mech Energy?Your car begins to roll down a hill, because you accidently left your parking brake OFF! You push on it trying to stop it, but it keeps moving at a constant velocity down the hill. (ignore friction acting on the car). Is mechanical energy conserved?A. YesB. NoC. Can’t be determined

Conservation of Mech Energy?Starting from rest, Tarzan down on swings on a vine. (ignore air resistance) Is mechanical energy conserved?A. YesB. NoC. Can’t be determined

Conservation of Mech Energy?Two cars are rolling in neutral (ignore friction) and crash into each other. Is mechanical energy conserved of the two cars?A. YesB. NoC. Can’t be determined

Conservation of Mech Energy?Two carts are rolling towards each other (ignore friction). One has a spring bumper, causing them to bounce off each other. Is mechanical energy conserved for the system of the two carts?A. YesB. NoC. Can’t be determined

Energy AnalogiesBar charts:

Money:

Mech Energy Bar chartsA sled slides up an iced embankment until it momentary stops at the highest point (ignore friction). Sketch the energy bar charts starting at the bottom and ending at the top.

KE + PEg = ME KE + PEg = ME

Initial Final

Changes in EnergiesA sled slides up an iced embankment until it momentary stops at the highest point (ignore friction). How did the change in KE compare to the change in PEg ?A. KE lost more than PEg gainedB. KE lost less than PEg gainedC. KE lost the same as PEg gainedD. KE gained the same as PEg lostE. None of these

Mech Energy Bar chartsYour car starts at rest and begins to roll down a hill, because you accidently left your parking brake OFF! (ignore friction). You push on it trying to stop it. Sketch the energy bar charts starting at the top and ending before you stop.

KE + PEg = ME KE + PEg = ME

Initial Final

Changes in EnergiesYour car starts at rest and begins to roll down a hill, because you accidently left your parking brake OFF! (ignore friction). You push on it trying to stop it. How did the change in KE compare to the change in PEg ?A. KE gained more than PEg lostB. KE gained less than PEg lostC. KE gained the same as PEg lostD. KE lost less than as PEg lostE. None of these

Mech Energy Bar chartsTarzan down on swings on a vine. (ignore air resistance) You push on it trying to stop it. Sketch the energy bar charts starting midway down through the swing and ending at the lowest point.

KE + PEg = ME KE + PEg = ME

Initial Final

Changes in EnergiesStarting from rest, Tarzan down on swings on a vine. (ignore air resistance) How did the change in KE compare to the change in PEg ?A. KE lost more than PEg gainedB. KE lost less than PEg gainedC. KE lost the same as PEg gainedD. KE gained the same as PEg lostE. None of these I

Conservation of Mechanical EnergyYou throw a 2kg rock at 25m/s @ 30⁰ off a 10m high cliff. How fast is it going when it hits the ground?

KE + PEg = ME KE + PEg = ME

Initial Final

Steps for Setting up Consrv of ME1. Pick initial & final positions2. Choose ground zero (h=0): lowest point that you

care about to solve the problem3. Determine if ME is conserved or not.

a. If it is conserved: MEinitial = MEfinal

b. If it is NOT conserved: MEinitial ≠ MEfinal

4. Determine which type of energies are present only at the initial and final positions

a. KE is it moving?b. PEg is it above ground zero?

5. Plug in numbers and solve and sketch bar charts

Conservation of Mechanical EnergyA rollercoaster is going at 1m/s at the top of a 20m hill, then plunges down and races back up a loop. How fast is it going at the top of the 15m high loop, if friction is ignored?

KE + PEg = ME KE + PEg = ME

Initial Final

4 Colored TracksAll the marbles are identical. If all start at rest from the same height at the same time, which marble will reach the end of the track first?A. BlueB. GreenC. YellowD. RedE. All will be the same

4 Colored TracksAll the marbles are identical. If all start at rest from the same height at the same time, which marble will be going the fastest at the end of the track?A. BlueB. GreenC. YellowD. RedE. All will be the same

Lesson 3: Springs & Elastic Potential Energy (PEe)

Demo: springs, bungee cord

SpringsWhat is Hooke’s Law for springs?

What does each variable represent and what are their units?

SpringsWhat would cause a spring to exert a greater force than another spring? (2 factors)

There are 2 springs, one had a high spring constant and the other had a low spring constant. What would the difference be if you tried to stretch each of them?

Elastic Potential Energy (PEe)What is the equation for Elastic Potential Energy (PEe)?

What is the unit for PEe ?

What does PEe describe?

Hooke’s LawDoes Hooke’s Law describe when springs are compressed or when springs are stretched?A. CompressedB. StretchedC. Either, it’s the sameD. Neither

Hooke’s LawA 22cm long spring is attached to a wall. When pushed horizontally with a force of 100N, the spring compresses to a length of 20cm. What is the value of the spring constant?A. 5 N/mB. 50 N/mC. 500 N/mD. 5,000 N/mE. None of these

Hooke’s LawA 5kg mass hangs at rest from a spring that is stretched by 0.15m. What is the spring constant of the spring?

Mechanical Energy

ME = KE + PEg + PEe

Conservation of Mech Energy?A bungee jumpers falls off the platform. Before he reaches the bottom, is mechanical energy conserved? (ignore air-resistance)A. YesB. Only during the initial free-fallC. NoD. Can’t be determined

Sketch the Energy Graphs at the followingpositions.

KE + PEg + PEg = ME

KE + PEg + PEg = ME

KE + PEg + PEg = ME

KE + PEg + PEg = ME

KE + PEg + PEg = ME

1

2

3

4

5

Steps for Setting up Consrv of ME1. Pick initial & final positions2. Choose ground zero (h=0): lowest point that you care

about to solve the problem3. Determine if ME is conserved or not.

a. If it is conserved: MEinitial = MEfinal

b. If it is NOT conserved: MEinitial ≠ MEfinal

4. Determine which type of energies are present only at the initial and final positions

a. KE is it moving?b. PEg is it above ground zero?c. PEe is spring stretched or compressed?

5. Plug in numbers and solve and sketch bar charts

A 2kg box is pushed against a spring with a spring constant of 5000N/m so that it is compressed by 10cm. If it is launched off a 3m high platform, how fast will it be going when it hits the ground?

Lesson 4: Mechanical Energy NOT Conserved

Bowling Ball Pendulum

When is ME not conserved?What would cause ME not to be conserved?

What is the Work done by a nonconservative force equal to in terms of energy?

When is ME not conserved?If ME is not conserved, does it remain constant or does it change?

What does the “change in” anything equal to? (what? minus what?)

Use this to write a mathematical expression for change in mechanical energy.

Rearrange this equation so that there are no minus signs (which is very helpful for not making careless math errors).

When is ME not conserved?

If ΔME is positive, what does that mean happened to the ME of the object?

How would a nonconservative force act on the object to cause ΔME to be positive?

When is ME not conserved?

If ΔME is negative, what does that mean happened to the ME of the object?

How would a nonconservative force act on the object to cause ΔME to be negative?

Conservation of Mechanical Energy?A Nerf ball is thrown straight up and it is affected by air resistance. As it goes up, the Work done on the ball by air resistance isA. PositiveB. NegativeC. Work is done, but whether it is positive or

negative can’t be determinedD. No Work is doneE. None of these can be determined

Conservation of Mechanical Energy?A Nerf ball is thrown straight up and it is affected by air resistance. As it goes up, Mechanical EnergyA. IncreasesB. DecreasesC. Is ConservedD. Can’t be determined

Conservation of Mechanical Energy?A Nerf ball is thrown straight up and it is affected by air resistance. As it goes up, what is the sign of ΔME?A. +B. – C. 0D. Can’t be determined

Conservation of Mechanical Energy?A Nerf ball is thrown straight up and it is affected by air resistance. Sketch the Energy Bar Charts 1: when ball is released; 2: as it is half way up; 3: when it is at the highest point.

KE + PEg + ΔME = ME KE + PEg + ΔME = ME KE + PEg + ΔME = ME

Conservation of Mechanical Energy?A Nerf ball is thrown straight up and it is affected by air resistance. As it comes down, the Work done on the ball by air resistance isA. PositiveB. NegativeC. Work is done, but whether it is positive or

negative can’t be determinedD. No Work is doneE. None of these can be determined

Conservation of Mechanical Energy?A Nerf ball is thrown straight up and it is affected by air resistance. Sketch the Energy Bar Charts 1: at the highest point; 2: as it is half way down; 3: when it about to be caught

KE + PEg + ΔME = ME KE + PEg + ΔME = ME KE + PEg + ΔME = ME

Conservation of Mechanical Energy?A Nerf ball is thrown straight up and it is affected by air resistance, and then caught at the same height from which it was released. Which is greater?A. The initial speed it had when it was thrown B. The final speed right before it was caughtC. Both are the sameD. Can’t be determined

Conservation of Mechanical Energy?You are doing a workout at Slater Hill by running up it. At the bottom you are going the fastest, but over time you slow down until at the top you stop. Sketch the Energy Bar Charts when you are at 1:the bottom; 2:half-way up;3: the top.

KE + PEg + ΔME = ME KE + PEg + ΔME = ME KE + PEg + ΔME = ME

Conservation of Mechanical Energy?You are doing a workout at Slater Hill by running up it. At the bottom you are going the fastest, but over time you slow down until at the top you stop. The Work done on you by your muscles wasA. PositiveB. NegativeC. Work is done, but whether it is positive or

negative can’t be determinedD. No Work is doneE. None of these can be determined

Conservation of Mechanical Energy?You are doing a workout at Slater Hill by running up it. At the bottom you are going the fastest, but over time you slow down until at the top you stop. As you go up the hill, what are the signs of the following changes in energies?

ΔKE ΔPEg ΔME

A. 0 0 – B. + – 0C. + – +D. + – – E. – + –

Conservation of Mechanical Energy?Your little cousin jumps on a slide and slides down. Friction is present and he didn’t start at rest, but he did speed up. What are the signs of the following changes in energies?

ΔKE ΔPEg ΔME

A. 0 0 – B. + – 0C. + – +D. + – – E. – + –

Conservation of Mechanical Energy?Your little cousin jumps on a slide and slides down. Friction is present and he didn’t start at rest, but he did speed up. Which is a true statement?A. KE gained more than PEg lostB. KE gained less than PEg lostC. KE gained the same as PEg lostD. KE lost less than as PEg lostE. None of these

Steps for Setting up Consrv of ME1. Pick initial & final positions2. Choose ground zero (h=0): lowest point that you care

about to solve the problem3. Determine if ME is conserved or not.

a. If it is conserved: MEinitial = MEfinal

b. If it is NOT conserved: MEinitial + ΔME = MEfinal

4. Determine which type of energies are present only at the initial and final positions

a. KE is it moving?b. PEg is it above ground zero?c. PEe is spring stretched or compressed?

5. Plug in numbers and solve and sketch bar charts

An 0.6kg water balloon is shot up at an angle out of a water balloon slingshot. The slingshot has a spring constant of 300N/m and is stretched by 0.9m. How fast is it going when it is 10m off the ground if it has lost 40J due to air-resistance?

An 0.6kg water balloon is shot up at an angle out of a water balloon slingshot going 45m/s at 1m above the ground. How fast is it going when it is 10m off the ground if it has lost 40J due to air-resistance?

A 2000kg truck going 40m/s goes up a 30⁰ run-away truck ramp. How fast is it going after 100m if there is 5,000N of friction acting on it?

Conservation of Mechanical Energy?What is the difference between and ?