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Chapter 6 Power and Energy

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Chapter 6Power and Energy

What You Need to Know

Alta Physics

- 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

- Mechanical Potential Energy
- Energy of Position
- Gravitational
- Elastic

- Energy of Position
- Kinetic Energy
- Energy of Motion
- If it moves it has kinetic energy

- Energy of Motion
- 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

- Chemical

Alta Physics

- 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 = (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

- 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 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

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 = Work/time = Joules/Second
- Mathematically there are two formulas for Power:

or since

then

Alta Physics

- 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

- Work
- Work at an angle
- Kinetic Energy
- Gravitational Potential
- Elastic Potential
- Conservation
- Power

Alta Physics