Transcript
WORK AND ENERGY
Definition of Work
Work is defined as a force exerted through a distance.
Whenever work is done, energy is transferred from one object to another or transformed from one form to another.
To calculate the work done, we multiply the applied force times the distance moved in the same direction as the force.
The equation used to calculate the amount of work done is:
W = F · D
where W is the work done, F is the force applied, and D is the distance moved in the direction of the force.
In the metric system, the unit of force is the Newton and the unit of distance is the meter. A force of one Newton exerted through a distance of one meter is called a Joule which is the metric unit of work. In the English system, a force of one pound exerted through a distance of one foot is known as a foot pound and is the basic unit of work.
Example
A worker pushes horizontally on a crate with a force of 300 N and the crate moves 5.0 m. How much work was done?
When we use the phrase that work is being done against something we mean that the applied force is equal but opposite to the force being opposed. Work done against gravity means a force equal to the weight of the object being lifted is applied over a vertical distance. Work done against friction means the applied force is equal to the frictional force but moves in the direction opposite to the frictional force.
Kinetic Energy and Potential Energy
Energy is defined as the ability to do work. Another way to look at the concept of energy is that it has the ability to cause a change in the motion, condition or position of an object. The metric unit of energy is the Joule.
In this section we will consider mechanical energy which is composed of kinetic energy and certain types of potential energy
Kinetic energy is energy associated with motion. It is calculated using the formula:
Ek = ½mv2
where Ek is the kinetic energy, m is the mass of the object and v is the speed of the object. In the classical sense, the object must have a mass and speed to have kinetic energy. The unit of kinetic energy is the Joule.
The work done on an object is equal to its change in kinetic energy.
Example
A 1.0 kg ball is fired from a cannon. What is the change in kinetic energy of the ball as it goes from 4.0 m/s to 8.0 m/s?
An application of this concept involves stopping a car. To bring a car to a stop, the brakes must convert the kinetic energy of the car into heat energy. The force of friction must be applied over a distance.
If we double the speed of a car from 20mph to 40 mph, the fact that the speed is squared in the kinetic energy formula means the kinetic energy of the car is now four times as much. This means the brakes must do 4 times the work. If the braking force is constant, the stopping distance now is 4 times as great. That is why any speeding in a school zone is dangerous.
Potential energy is the energy an object has because of its position, location, or condition. If work must be done to change one of these, we say there is a change in the potential energy.
Lifting an object to a higher position requires that work be done. This work is stored in the lifted object as gravitational potential energy. The equation used to calculate work done against gravity is:
W = mgh
GPE = mgh
where W is the work done, m is the mass of the object lifted, g is the acceleration due to gravity, h is the distance the object is lifted, and GPE is the gravitational potential energy. The unit of potential energy is also the Joule.
Example
How much potential energy is given to a 4.0 kg concrete block that is lifted a distance of 2.0 m?
Gravitational potential energy is often considered to be zero on the surface of the earth. In this case, the surface of the earth is called our reference point. It is chosen because it is the most convenient zero point in many cases. An object in a hole in the ground would have a negative gravitational potential energy since some work would be done in bringing it up to the surface. Remember that the reference point is arbitrary and can be chosen so that it simplifies the situation.
Conservation of Energy
The Law of Conservation of Energy states that energy can be neither created or destroyed. When energy is changed from one form to another it is conserved.
The total energy of an isolated system remains constant.
An isolated system is something that is not affected by anything that is not part of it.
When we consider conservation of mechanical energy, we only include kinetic energy and the appropriate form(s) of potential energy. If we consider a situation where gravity is the only force involved, we can use the equation:
Initial Energy = Final Energy
(Ek + Ep)1 = (Ek + Ep)2
(½mv2 +mgh)1 = (½mv2 +mgh)2
where the subscript 1 indicates the initial energy conditions and the subscript 2 indicates the final energy conditions.
Example
An object is dropped from a height of 12 m. What is its speed when it has fallen half the distance?
The exception to the above discussion occurs during nuclear reactions when a signifigant amount of matter is changed to energy or energy to matter. Since matter and energy are different forms of the same thing, it is more accurate to describe conservation of matter and energy together.
Power
Power is defined as the time rate of doing work or using energy.
The equations for power are:
P = W/t
P = Fd/t = FV
where P is power, W is work, t is time, F is force, d is distance, and V is speed.
The basic unit of power is the J/s which is called a watt(w).
Example
A student who weighs 556 N climbs a vertical height of 4.0 m in 25 seconds. Find (a) the work done and (b) the power output of the student.
Be careful not to confuse the symbol for watt(w) with the letter variable used for work(W).
In the British system the unit of power is the foot pound per second. We use a larger unit, the horsepower(hp) for engines.
1 horsepower(hp) = 550 ftlb/s = 746 w
Energy consumed can be calculated using the power equation if we know the power consumption of the device and the time it is in use. The equation is:
E = P · t
where E is the energy used, P is the power used and t is the time over which it is used. The resulting unit is a Joule. If we express power in kilowatts(1000 watts) and time in hours, we get a unit used in calculating power company bills, the kilowatthour(kwhr).
Example
A household uses 2.0 kw of power 24 hours a day for 30 days. If electricity costs $.08 per kwhr, what is the electric bill for the month?
Forms and Sources of Energy
The forms of energy that we will consider are briefly defined here.
Mechanical Energy is kinetic energy and energy associated with motion or position such as Gravitational Potential Energy.
Thermal or Heat energy is energy associated with motion of the individual molecules of a substance or object.
Electrical Energy is associated with the motions of electric charges as in electric currents.
Chemical Energy is energy associated with the formation and breaking of chemical bonds in fuels and other applications.
Radiant Energy is energy associated with electromagnetic radiation such as light from the sun or microwaves.
Nuclear Energy is released during fission and fusion reactions when small amounts of matter are converted into relatively large amounts of energy.
The source of energy for our bodies is the food we eat. We actually give off heat energy at the rate of a 100 w light bulb.
The main commercial sources of energy are coal, oil, and natural gas(fossil fuels). The use of nuclear, hydroelectric, and other renewable energy sources has increased over the last several decades.
Energy consumption for the year 2000 is shown in the bar graph below.
The U.S. accounts for 5% of the world's population, but consumes 25% of the world's energy. Since the use of fossil fuels and nuclear energy sources gives rise to pollution and environmental concerns, nonpolluting fuels and energy sources are being developed.
Alternative Fuels and Sources of Energy
A newly discovered low polluting fuel that is being researched is methane hydrate which is described as ice that burns. It is estimated that the energy available in all the methane hydrate is equal to twice the energy stored in all of the world's fossil fuel reserves. Research on extraction and use is underway.
Hydropower produces electricity with practically no pollution. Problems are most of the best dam sites have been developed. Flooding behind the dam ruins agricultural land and ecosystems.
Gasohol, a mixture of ethanol and gasoline can be used in properly equipped vehicles. Problems are its use does not reduce production of pollution and twice as much energy is used in its manufacture than it produces.
Wind Power is nonpolluting and has been used for centuries. Problems are lack of land appropriate for wind energy farms and the inconsistency of the wind.
Solar Power uses energy directly from the sun to supply heat or light. This energy can also be stored in thermal masses to be released later. Photovotaic cells can convert sunlight into electricity which can be used immediately or stored in batteries or capacitors for later use. Problems are efficiency(only about 25% to 30%) and cost of the electricity. Solar generated electricity costs about $.30 per kwhr compared to that generated by fossil fuels at $.08 per kwhr.
