1. Chapter 6 Power and Energy
What You Need to Know
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2. 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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3. 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
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4. 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.
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5. 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)
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6. 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
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7. 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
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8. 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
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9. 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.
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10. 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
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11. 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
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12. 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
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13. 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
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14. 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.
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15. 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.
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16. 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
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17. Power Power = Work/time = Joules/Second
Mathematically there are two formulas for Power:
or since
then
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18. 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
= Watts
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19. Problem Types Work Work at an angle Kinetic Energy
Gravitational Potential
Elastic Potential
Conservation
Power
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