Energy, Work, & Power

SP3. Students will evaluate the forms and transformations of energy.

a. Analyze, evaluate, and apply the principle of conservation of energy and measure the components of work-energy theorem by

• describing total energy in a closed system.

• identifying different types of potential energy (PE).

• calculating kinetic energy (KE) given mass and velocity.

• relating transformations between PE and KE.

f. Analyze the relationship between temperature, internal energy, and work done in a physical system.

g. Analyze and measure power.

What is energy & why do we need it?

• Energy – the ability to do work
• Work – moving an object by exerting a force
• Force – a push or a pull
• Whenever force is used to move an object, energy is required
• EX. When you walk, your muscles pull on your bones in order to move your body. This requires your muscles to use energy.

What is energy & why do we need it?

• Without energy, there could be no motion
• Atoms and molecules could not move
• Stars could not shine
• Planets could not orbit around stars
• Animals could not walk, run, swim, or fly
• The wind could not blow
• Messages could not be sent from your brain to your body

Is work being done when you hold a book over your head?

• No
• But it did take work to get it there
• Whenever work is being done, energy is being used
• The energy was transferred from your body to the book

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How much work is being done?

• We can measure the amount of work being done to move an object
• We need to know 2 things in order to measure work:
1. The amount of force being used
2. The distance of the movement
• We can calculate work using the following formula:

Work = Force x Distance (W = F d)

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Calculating Work – Which Units?

• When calculating work, use the following units:
• Force is measured in newtons (N)
• Distance is measure in meters (m)
• Work is measured in joules (J)
• 1 joule equals 1 newton multiplied by 1 meter
• You do about 1 joule of work when you lift an apple above your head

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Calculating with Work –Problem #1

• If you lift a 3 N book 2 meters off the floor, how much work did you do?
• W = F x d
• W = 3N x 2m
• W = 6 J

Calculating with Work –Problem #2

• A man pushes a couch a distance of 0.75 m. If 113 J of work is done, what is the magnitude of the force applied??
• F = W ÷ d
• F = 113 J / 0.75 m
• F = 151 N

Calculating with Work –Problem #3

• It requires 3480 J to move a 675 N object how far?
• d = W ÷ F
• d = 3480 J / 675 N
• d = 5.16 m

Calculating with Work –Problem #4

• The 3^rd floor of a house is 8 m above street level. How much work is needed to move a 150 kg refrigerator to the third floor?
• W = Fd
• F = mg (150 kg x 9.8 m/s²)=1470 N
• W = 1470 N x 8 m
• W = 11760 J

Calculating with Work –Problem #5

• A toy truck is pushed across a table 0.80 m north and pulled back 0.80 m south. If a constant horizontal force of 15 N was applied in both directions, what is the net work?
• Displacement = 0 (same distance N and S)
• No motion = no work done

Question

• When you carry a heavy bag of groceries from your car to your kitchen, what does work, your arms or your legs? Explain why.
• Your legs, because they move you and the groceries from the car to the kitchen. Your arms only lift and hold the groceries.

Energy Is Also Measured In Joules

• Since energy is required to do work, it is measured using the same unit (joules)
• The amount of energy required to do work is ALWAYS greater than or equal to the amount of work being done
• EX. If you do 6J worth of work to lift a book, you need at least 6J of energy to do it

Doing Work Gives Energy to Objects

• When work is done on an object:
• Energy is transferred from the object doing the work to the object having work done on it
• The object doing the work loses energy
• The object having work done on it gains energy
• EX. A student pushing a desk across the floor is doing work on the desk – energy is transferred from the student to the desk and the student loses energy

Why do we get tired after doing work?

• We give up our energy to all the objects we touch and move around
• In any energy transfer in our body, some energy is changed to heat and transferred to our environment – the energy is LOST from our body
• Staying alive requires a lot of energy
• Heart beating, brain sending messages, cells moving substances in and out, muscle contractions, etc.
• As our body’s energy gets low, we get tired

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What is power?

• Power – the rate at which work is done
• More power means…
• More work is done in the same amount of time
• The same amount of work is done in less time
• EX. A person that is a more powerful runner is faster and can run farther in the same amount of time as a less powerful runner (more work in equal time)
• EX. A car with a more powerful engine can accelerate to 60mph faster than a car with a less powerful engine (equal work in less time)

Calculating Power

• Power is measure in watts (W)
• We need to know 2 things in order to measure power:
1. The amount of work being done
2. The amount of time it takes to do the work
• We can calculate power using the following formula:

Power = Work / Time (P = W / t)

• 1 watt equals 1 joule divided by 1 second

Calculating Power – Sample Problem 1

• If an engine does 100,000 joules of work in 10 seconds, how much power did it use?
• P = W / t
• P = 100,000J / 10s
• P = 10,000W
• The engine used 10,000 watts of power

Calculating Power – Sample Problem 2

• Because work equals force multiplied by distance, another way to write the power formula is:

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Power = (Force x Distance) / Time

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P = (F x d) / t

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• P = W / t is the same as P = (F x d) / t

Calculating Power – Sample Problem 2

• If an engine exerts 3500 newtons of force to move a car 50 meters in 10 seconds, how much power did it use?
• P = (F x d) / t
• P = (3500N x 50m) / 10s
• P = 175,000J / 10s
• P = 17,500W
• The engine used 17,500 watts of power

A Watt Measures Work Done and Energy Used In an Amount of Time

• A Watt equals 1 Joule per second
• The more watts, the more work is done each second
• Joules also measure energy, so a watt also measures energy use per second
• EX. A 100W light bulb uses 100J of energy each second that it is on

More about Energy

Different Forms of Energy

1. Electrical
2. Chemical
3. Radiant
4. Thermal
5. Mechanical

KINETIC ENERGY (KE)

-The energy of MOTION

-All moving objects have Kinetic Energy!

-Depends on: MASS and SPEED of the object

-Equation:

Kinetic Energy (KE) = ½ x mass x velocity squared

KE = 1/2mv²

-Joule (J) = SI unit for Energy

Sample Problem

-A jogger whose mass is 60kg is moving at a speed of 3 m/s. What is the jogger’s Kinetic Energy?

Mass = 60kg

Velocity = 3 m/s

KE = ??J

KE = 1/2mv²

KE = 1/2(60kg)(3m/s)²

KE = 270 J

POTENTIAL ENERGY (PE)

-The energy of REST

-Objects at REST have POTENTIAL ENERGY

-Potential Energy is CHANGED into KINETIC ENERGY when MOTION occurs

TYPES OF POTENTIAL ENERGY

1. Elastic Potential Energy = Energy stored by something that can be STRETCHED or COMPRESSED

Ex: Rubber band

2. Chemical Potential Energy = Energy stored in CHEMICAL BONDS

Ex: Food, Natural gas

3. Electrical Potential Energy = Energy stored due to ELECTRICAL CHARGES

4. Nuclear Potential Energy = Energy stored in the NUCLEI OF ATOMS

TYPES OF POTENTIAL ENERGY

5. Gravitational Potential Energy: Energy stored by objects due to their POSTION ABOVE EARTH

-Ex: Anything with the potential to FALL

-Depends on: MASS and HEIGHT above ground

-Equation:

GPE (J) = Mass (kg) X gravity (m/s²) X height (m)

GPE = mgh

GPE Example Problem

-What is the GPE of a ceiling fan that has a mass of 7kg and is 4m above the ground?

GPE = mgh

Gravity = 9.8 m/s²

Mass = 7 kg

Height = 4 m

GPE = (7kg)(9.8m/s²)(4m)

= 274 kgm²/s² = 274 J

To INCREASE GPE

1: INCREASE object’s HEIGHT

2. INCREASE object’s MASS

The Change of GPE to KE

-As objects fall, GPE is changed into KE

-KE is LARGEST right before the object hits the ground, thus GPE is the SMALLEST right before hitting the ground

-Objects with MORE GPE move FASTER because they have more KE

Converting between KE and PE

-MECHANICAL ENERGY = Total amount of POTENTIAL and KINETIC energy in a system

Mechanical energy = PE + KE

What happens to the mechanical energy as PE and KE are converted into each other?

ME stays the same!! As PE and KE are converted, the FORM of energy changes, but the TOTAL AMOUNT STAYS THE SAME

The Law of Conservation of Energy

-States that: ENERGY CAN’T BE CREATED OR DESTROYED!!

-So does this mean the total amount of energy in the Universe is the same at all times???

Friction and Air Resistance

These forces can cause some mechanical energy to change into THERMAL ENERGY!!