This wiki has been stolen by Joyce, Ashlyn, and Victoria :O

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Joyce: power and efficiency

Ashlyn: energy, problems, kinetic energy

Victoria: temperature etc., relations etc

What is work?


Work is a transfer of energy from one object to another and the object that exerts the force does the work. By definition, work is the product of the forces exerted on an object and the distance the object moves in the direction of the applied force thus giving the equation W=Fd and is measured in joules (J). This means that an action can only be considered to be work if both the direction of the applied force and direction of travel are the same. An example of this would be pushing an object along a flat surface. Since in this specific situation the movement of travel is determined by the direction of the applied force, the action is considered to be work. If the force exerted is perpendicular to the direction of motion, work is not done an example being an object carried up the stairs. Since the applied force is upwards and the direction of travel is horizontal, they do not share the same direction and thus work is not done. Although physical work is being completed, the object does not gain energy so no work is done.

Example 1: How much work is being done if a student lifts a box of books that weighs 185N and walks 10 m?
ex.jpg
A: no work is done because the direction of movement and the direction of the applied force are not the same.

Example 2: How much work is being done if a student lifts a box of books that weighs 185 N 1.20 m from the ground?
Since both the applied force and direction of movement are in the same direction, there is a transfer of energy and work is done.
F=185N
d=1.2m

work2.jpg
A: the student does 222J of work

The amount of work done also depends on the angle of the applied force. If you push a lawn mower, the applied force is at an angle and the handle which you are pushing has two components, vertical and horizontal. Since the vertical component is perpendicular to the ground, it does no work which means only the horizontal component does work. Work done with an applied force at an angle to the motion is found by multiplying the force by the cosine of the angle between the applied force and the direction of motion and by the distance traveled.

work_at_an_angle.png

Example 3: A sailor pulls a boat along a dock using a rope at an angle of 55.0o with the horizontal. How much work is done by the sailor if he exerts a force of 260 N on the rope and pulls the boat 35.0m?
angle_example.png
A: the sailor does 5.22x103 J of work

What is power?

Power is a rate that work is done or the rate of energy conversion. It is defined by the equation power.pngwhere W represents work and t is time.The units of power is Joules per second or watts (W).
Note: recall that W=Fd (F - force (N), d - distance (m)) so the definition of power could also be this: power2.png

Example 4: Johnny needs to push a box with a mass of 35.0 kg 50.0 m in 80 seconds. How much power does he need to do this task?

, we must convert the mass of the box into weight to calculate work:
work.png
Then we plug in the values to solve for P:
power.jpg
A: Johnny needs 214W to push the box
Average power can be determined by using the equation average_power.png. This is because the change of work over the change of time results in the average amount of work done in a chosen unit of time.

Example 5: Adam pulls a wheelbarrow with a weight of 400 N that is carrying 5.0 kg of books for 30 m at an angle of 45o from the ground and is walking with an initial velocity of 1 m/s. He then sees a book on the road 20 m ahead of him and runs with a velocity of 2.5 m/s to pick it up.
A) How much work does Adam need to pull the wheelbarrow and books before he sees the book on the ground?
B) How much work does Adam need to pull the wheelbarrow and books when he runs towards the book on the ground?
C) How much time does Adam take to walk the first 30 m?
D) How much time does Adam take to reach the book on the ground from when he starts running?
E) What is the average power that Adam exerts during this situation?

work2.png

Power can also be measured in a different unit other than watts. Since 1J is relatively small compared to the amount of work done by even the simplest machines in a day we use the kilowatt hour to measure work in larger units. A kilowatt hour represents the amount of work done by a machine with the power of 1kW in 1h. This is how we calculate the work done in 1 h working at the rate of 1kW:
kW.png
Utilize the kilowatt hour instead of watts and seconds to when needing to calculate work in kilowatt hours.

Example 6: How much work in kilowatt hours is done by a 6000 W electric generator, running 8.0h a day for a year?
kW_example1.png

Example 7: How long in hours will it take a 500W power drill to do 100kWh of work?
kW_example2.png

Example 8: How much power is being developed by a machine that can do 600kWh of work in 12h?
kW_example3.png

What is efficiency?


The Law of Conservation of Energy states that the amount of energy present before energy transformation is equal to the energy present after energy transformation. At times, some of the energy is converted to other forms such as thermal energy other than the mechanical energy that we are able to visualize. The efficiency of an object is determined by its ability to convert the initial amount of energy, the input, into the final output energy and is a ratio of output work to input work.
efficiency.png
The larger the percentage, the more efficient the object or system is at converting energy. An example of an object that is inefficient is an automobile. Suppose the fuel fed into the automobile's engine has 1000J of chemical energy. In the internal combustion engine, the fuel is vaporized and mixed with air in the carburetor, then drawn into a cylinder containing a piston. A spark from the spark plug ignites the fuel mixture, producing very high temperatures and pressures which produces gases and pushes down on the piston that turns the crankshaft, and thus, through the transmission, turns the wheels and makes the car move forwards. A majority of the input energy is lost as thermal energy such as the heat being carried away by the exhaust gases and through the walls of the cylinders in the engine. In addition, to prevent the engine from overheating, energy is used to run a water pump and fan to keep the engine cool so while energy is ultimately transferred to the wheels of the car, a lot of the input energy goes into running the engine and keeping it cool. By the time all these losses have been subtracted from the input energy, perhaps only 250 of the original 1000J reaches the transmission and only 100J is delivered to the wheels. The other 900J is transferred into thermal energy thus making an automobile only 10% efficient.
efficiency_diagram.png



Example 9: How much work can a 22kW car engine do in 60s if it is 100% efficient?
100% efficiency implies that the output work is equivalent to the input work. This means that 100% of the energy produced by the engine is converted into energy used to make the car move.

efficiency_example.png

Everyday objects range in efficiency with some being extremely efficient and others being highly insufficient. Efficiency helps us determine which common machines require the least amount of energy to operate since an efficient object can do more work with the same amount of applied energy than an object with less efficiency. An example of this would be the comparison of LED lights and incandescent lamps. Both are sources of light and provide us with a means to see in the dark but LED lights are approximately 18x more efficient than incandescent lamps since LED lights are 90% efficient and incandescent lamps are 5% efficient. While electrical energy is used to power both these light sources, 95% of the electricity in an incandescent lamp is converted into forms of energy other than light such as heat energy. This comparison ultimately means that in a given period of time, an incandescent lamp will use up 18x more energy than the LED light if both had the same light intensity. Therefore, if we purchase machines that are more efficient than older models or machines, we would be saving money by using less energy over time to power them for the same results as those older models and machines.

Here is a chart that compares the efficiency of some of our common machines:
Machine
Efficiency (%)
Electric Generator
99
Large Electric Motor
92
Dry Cell
91
Home Gas Furnace
85
Storage Battery
72
Home Oil Furnace
65
Small Electric Motor
62
Liquid Fuel Rocket
47
Steam Power Plant
41
Diesel Engine
38
Diesel Locomotive
35
Internal Combustion Engine
25
Fluorescent Lamp
20
Solar Cell
10
Steam Locomotive
5
Incandescent Lamp
4

Energy

ENERGY is the capacity to do WORK, and is measured in joules (J). There are many different forms of energy, including heat energy, mechanical energy, light energy, and sound energy.

Mechanical energy is the sum of the total KINETIC ENERGY and POTENTIAL ENERGY of an object. In a frictionless situation, mechanical energy is usually conserved, while kinetic energy and potential energy mirror each other.
For example, if a skier started at the top of a very tall mountain (high potential energy and no kinetic energy), then began skiing downhill and gaining speed (increasing kinetic energy and decreasing potential energy), then began decelerating as they went up another hill (decreasing kinetic energy and increasing potential energy), and no kinetic energy was lost due to friction or sound, mechanical energy would be conserved. The graph for this situation would look like this:

Kinetic Energy is calculated using the formula…


EKinetic = (1/2)mv2
Where m is the mass (kg)
v is the velocity (m/s)

Potential Energy is calculated using the formula…


EPotential = mgh
Where m is the mass (kg)
g is the force of gravity (9.8 m/s2)
h is the height of the object (m)

EXAMPLE PROBLEMS


1) A ball is rolling on the frictionless track shown below at 3 m/s when it is at point 1 (100 m above ground level). Its mass is 2kg. Point #2 is at ground level.



a) What is the total mechanical energy of the car at point #1?

Etotal = EK + EP
Etotal = ((1/2)mv2) + (mgh)
Etotal = ((1/2)(2kg)((3m/s)2)) + (2kg)(9.8 m/s2)(100 m)
Etotal = 1969 J

b) What is the total mechanical energy of the car at point #2?
Because the total mechanical energy is CONSERVED, the mechanical energy at point #2 is the same as at point #1: 1969 J.

c) How fast will the car be moving when it reaches point #2?

Ekinetic (i) + Epotential (i) = Ekinetic (f) + Epotential (f)
9 J + 1960 J = Ekinetic (f) + 0
Ekinetic (f) = 1969 J

1969 J = (1/2)(2kg)(v2)
V2 = 1969 J
V = 44.37 m/s

What is Temperature?

Temperature is a number directly proportional to the average kinetic energy in a substance. It is measured in degrees Kelvin.

For example, if you look at gas particles in room, and take the average kinetic energy, then multiply it by a conversion factor, you can find the temperature in Kelvins.

The temperature is not energy, but is directly proportional to it. Since it is proportional, when the average kinetic energy increases, the temperature also increases. Adding heat to the system will cause the temperature to rise. When a system has no heat, it reaches absolute zero and all molecular motion stops. Absolute zero would be the lowest theoretical temperature a material can have, since Kelvins are defined to be always positive. Temperature can be measured with a thermometer, which is able to determine the internal energy contained within a system.

What is Thermal Energy?


Thermal Energy is the total kinetic energy that results from the random movement of atoms and molecules in an object. The faster the atoms and molecules move, the higher the thermal energy. Thermal energy also depends on the body's mass as well as it's temperature. For example, a bath of ice water would have a greater thermal energy than a cup of boiling water.

Thermal Energy can be transferred the form of heat. Heat is Thermal Energy in ‘transfer’. Heat can be transferred in 3 forms, Radiation, Convection, and Conduction.

In conduction, the heat is transferred directly from one molecule to another. When molecules move fast, they vibrate and cause other molecules to vibrate quickly as well. Metal is a good example of a conductor.

Convection occurs when a heated gas or liquid is caused to move away from the source of heat, carrying energy with it and causing it to be less dense or increase in buoyancy. When it cools, it drops. This leads to a circulation of liquid or gas. Convection does not occur in solids, since molecules in a solid do not move freely.

When Thermal Energy is emitted by hot objects, it is called Radiation. This energy travels in electromagnetic waves. The Sun is able to emit thermal energy through the use of waves even in space, since, Radiation does not require any particles of matter.

What is Specific Heat Capacity?


The specific heat capacity can be defined as the amount of heat needed to raise a the unit mass of a substance by one degree Celsius.

The following are examples of various substances and their specific heat capacities.
Substance
Specific Heat Capacity (J / kg•C°)
Water (L)
4180
Aluminum
900
Iron
450
Alchohol
2400

Solving problems involving: mass , specific heat capaicty, and change in temperature.


Q=mcΔT
Q = heat/thermal energy (J)
m = mass (kg)
ΔT = temperature change (°C) or (K)
C = specific heat capacity

Example 1:What is the heat transfered from 540 kg of lead to its surrroundings as it cools from 825°C to 30°C? (the spceific heat capacity of lead is 130 J / kg•C°

Q=mcΔT
= (540) (130) (825-30)
= 5.58 x 10-7
Example 2: 0.475 kg of metal that is at 95°C is placed in wate causing 1.35x104 J of heat to be transferred to the water. The final temp of both the metal and water is 23°C. Find the specific heat capacity of the metal.
Q=mcΔT
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Law of conservation of Energy

The Law of conservation of Energy states that energy cannot be destroyed or created, only transformed. The total amount of energy in a system remains constant over time. Examples of energy transformation include ; Heat --> Electric energy (Thermoelectric) andChemical Energy --> Heat and Light (Fire).

Resources
Power solver (force, time and distance values can be manipulated)
Power solver (equations can be manipulated)
Hyperphysics
The Physics Classroom
Practice Quiz