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# Chapter 6 Power and Energy - PowerPoint PPT Presentation

Chapter 6 Power and Energy. What You Need to Know. Energy Facts. There are different types of energy Energy of all types is measured in Joules Law of Conservation of Energy – Energy can be neither created nor destroyed, merely changed from one form to another.

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Chapter 6 Power and Energy

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## Chapter 6Power and Energy

What You Need to Know

Alta Physics

### Energy Facts

• There are different types of energy

• Energy of all types is measured in Joules

• Law of Conservation of Energy – Energy can be neither created nor destroyed, merely changed from one form to another

Alta Physics

### Types of Energy(Unit Overview)

• Mechanical Potential Energy

• Energy of Position

• Gravitational

• Elastic

• Kinetic Energy

• Energy of Motion

• If it moves it has kinetic energy

• Heat Energy

• Heat is a form of Energy Transfer

• Other Forms of Stored Energy

• Chemical

• Fuels - usually release energy by combustion

• Food – energy released by digestion

• Electrical

• Generated from other forms of energy

Alta Physics

### Work

• The Physics definition of work requires a displacement, i.e. an object must be moved in order for work to be done!

• The Applied force which causes the displacement contributes to the work, i.e. in order to contribute to the work, the applied force must be parallel to the displacement.

Alta Physics

### Work: A Mathematical Definition

• Work = (Force)(Displacement)

• Units of Work = (Newton)(Meter)

• 1 Newton•Meter = 1 Joule

• A Joule is a unit of Energy and it takes energy to do work and work done on an object either causes it to move (kinetic energy) or is stored (potential energy)

Alta Physics

### Sample Problem

• What work is done sliding a 200 Newton box across the room if the frictional force is 160 Newtons and the room is 5 meters wide?

W = Ff • ΔX = (160 N)(5 m)

800 Joules

Alta Physics

### Kinetic Energy

• Kinetic Energy is energy of Motion

• Any moving object has kinetic energy

• Dependent on the mass of the object and its velocity.

• Mathematically expressed as:

Ek = ½ mv2

Alta Physics

### Sample Problem

• What is the kinetic energy of a car with a mass of 2000 kg moving at 30 m/s?

• Ek = ½ mv2 = (½)(2000 kg)(30 m/s)2

= 900,000 Joules

Alta Physics

### Energy of Position:Gravitational Potential Energy

• Occurs due to the accelerating force of gravity

• Is determined by the position of the object in the gravitational field

• Mathematically determined by: Ep = mgh where m is mass, g is the acceleration due to gravity and h is the height above a determined baseline.

Alta Physics

### Sample Problem

• What is the potential energy of a 10 kg rock sitting on a cliff 30 meters high? The acceleration due to gravity is 9.8 m/s2.

• Ep = mgh = (10 kg)(9.8 m/s2)(30 m)

2940 Joules

Alta Physics

### Elastic Potential Energy

• Bungee cords, rubber bands, springs any object that has elasticity can store potential energy.

• Each of these objects has a rest or “zero potential” position

• When work is done to stretch or compress the object to a different position elastic potential energy is stored

Alta Physics

### Elastic Potential Energy

• Top picture is “rest position”; x = 0

• This is a point where the elastic potential energy = 0

• Bottom picture is “stretched position”

• Here elastic potential energy is stored in the spring

• Ep = ½ kx2 where k is the “spring constant” in N/m

Alta Physics

### Sample Problem

• What is the Elastic potential energy of a car spring that has been stretched 0.5 meters? The spring constant for the car spring is 90 N/m.

• Ep = ½ kx2 = (½)(90 N/m)(0.5 m)2

=11.25 Joules

Alta Physics

### Where Does “K” Come From?

• K is measured in Newtons/meter. It is defined as the force required to displace a spring 1 meter. So:

K = F/x

• Often K is determined by hanging a known weight from the spring and measuring how much it is stretched from its rest postion.

Alta Physics

### Sample Problem

• A spring is hung from a hook and a 10 Newton weight is hung from the spring. The spring stretches 0.25 meters.

• What is the spring constant?

• If this spring were compressed 0.5 meters, how much energy would be stored?

• If this spring were used to power a projectile launcher, which fires a 0.2 kg projectile, with what velocity would the projectile leave the launcher? Assume 0.5 m compression.

Alta Physics

### Solution

K = F/x

K =10 N/0.25 m = 40 N/m

Ep = ½ Kx2

Ep = ½ (40 N/m)(0.5 m)2 = 5 Joules

Ep = Ek = ½ mv2

5 Joules = ½ (0.2 kg)(v2)

V = 7.05 m/s

Alta Physics

### Power

• Power = Work/time = Joules/Second

• Mathematically there are two formulas for Power:

or since

then

Alta Physics

### Sample Problem

• What power is developed by a 55 kg person who does 20 chin ups, h = 3 m, in 45 seconds?

• P= w/t = FΔd/t = mgh/t

(20(55 kg)(9.8 m/s2)(3 m))/45 sec

= 718.6 Watts

Alta Physics

### Problem Types

• Work

• Work at an angle

• Kinetic Energy

• Gravitational Potential

• Elastic Potential

• Conservation

• Power

Alta Physics