Work & Energy
When an object has been moved from one point to another,
work has been done.
Work
force x distance
Energy
the ability to do work
Energy is most evident when it is being transferred
or transformed. That is, when work is being done.
Potential and Kinetic Energy
Potential Energy
Potential Energy is stored energy
weight
(force of gravity) |
= Newton, N
= mass x gravity
= kg x m/s2 |
| mass |
= kilograms, kg |
| gravity |
= m/s2 |
| height |
= meters, m |
|
Gravitational Potential Energy
Potential Energy that is due to elevated position
PE = weight x height
PE = mass x gravity x height
If mass, gravity or height increases, Potential Energy
increases.
If an object has Potential Energy, it has the ability
to do work.
The SI unit of energy is the Joule.
Joule
The energy needed to raise 1 N by 1 m straight up.
1 Joule = 1 N x 1 m
or
Joules = kg x m/s2
x m
or
Joules = mass x gravity x height
Example:
How much Potential Energy, in Joules, does a diver weighing
100 Newtons have at the top of a platform 100 meters in the air?
PE = Weight x height
PE = 100 N x 100 meters
PE = 10,000 N x m
(Remember that 1 N = 1 kg x m/s2)
PE = 10,000 kg x m/s2
x m
(Remember that 1 Joule = 1 kg x m/s2
x m)
PE = 10,000 Joules
Kinetic Energy
Kinetic Energy is the energy of motion
Any mass that is moving has kinetic energy
If an mass is moving, then it is capable of doing
work.
The kinetic energy of an object depends on the mass of
an object as well as its velocity. It is equal to ½ the
mass of the object multiplied by the square of the speed:
KE = ½ mass x speed2
Since the speed is squared,
it turns out that
If the speed of an object is doubled,
then its kinetic energy is quadrupled.
This means,
four times the work is required to double the speed.
Example:
First,
What is the Kinetic Energy, in Joules, of a car with
a mass of 1000 kilograms moving at a speed of 10 meters per second?
KE = ½ 1000 kg x (10 m/s)2
500 kg x 100 (m/s)2
50,000 kg x (m/s)2
or
KE = 50,000 kg x m/s2
x m
so that
KE = 50,000 Joules
Second,
What happens to the Kinetic Energy, in Joules, when the
speed of the car with a mass of 1000 kilograms doubles its speed to 20
meters per second?
KE = ½ 1000 kg x (20 m/s)2
500 kg x 400 (m/s)2
200,000 kg x (m/s)2
or
(Rearrange the terms by pulling out the
meter)
KE = 200,000 kg x m/s2
x m
(Remember that 1 Joule = 1 kg x m/s2
x m)
so that
KE = 200,000 Joules
As you can see, when the speed of the car was doubled,
the Kinetic Energy quadrupled.
That is,
Four times as much work was required to make the car
go twice the speed.
What is the difference between
Potential and Kinetic Energy?
Practice Problems
Answer the following questions: |
|
| 1. |
Are the following examples of Potential or
Kinetic energy? |
|
.
| a) gasoline |
b) skating |
c) a candy bar |
| . |
|
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| d) a stretched rubber band |
|
|
| . |
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| 2. |
What is happening to the potential energy
of a rock climber going up a mountain? |
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| 3. |
What is happening to the potential energy
of a rock climber coming down a mountain? |
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Heat and Units of Energy
Heat
The energy associated with the motion of particles
in a substance
SI Unit of Energy
joule J
kilojoule kJ 1,000 joules
calorie (cal)
The calorie
Originally defined as
the amount of energy needed to raise the temperature
of one gram of water by 1 °C.
Now,
1 calorie is defined as exactly 4.184 J.
Conversion factor:
1 cal = 4.184 J
1 kilocalorie (kcal) is equal to 1,000 calories
and
1 kilojoule (kJ) is equal to 1,000 joules
How does heat relate to energy?
Practice Problems
Answer the following questions: |
|
| 4. |
When 1.0 gram of gasoline burns in an automobile
engine.
48,000 J are released. Convert this quantity of
energy to the following units: |
|
.
| a) calories |
| . |
| b) kilojoules |
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