Explain how the general definition of energy as the ability to do work makes perfect sense in terms of either form of mechanical energy. Discuss the law of conservation of energy and dispel any misconceptions related to this law, such is the idea that moving objects just slow down naturally.
Identify heat generated by friction as the usual explanation for apparent violations of the law. Try to get students to understand heat and temperature at a molecular level. Explain that energy lost to friction is really transforming kinetic energy at the macroscopic level to kinetic energy at the atomic level. We saw earlier that mechanical energy can be either potential or kinetic.
In this section we will see how energy is transformed from one of these forms to the other. We will also see that, in a closed system, the sum of these forms of energy remains constant. Quite a bit of potential energy is gained by a roller coaster car and its passengers when they are raised to the top of the first hill. Remember that the potential part of the term means that energy has been stored and can be used at another time.
You will see that this stored energy can either be used to do work or can be transformed into kinetic energy. For example, when an object that has gravitational potential energy falls, its energy is converted to kinetic energy. Remember that both work and energy are expressed in joules. Refer back to Figure 9. The amount of work required to raise the TV from point A to point B is equal to the amount of gravitational potential energy the TV gains from its height above the ground.
This is generally true for any object raised above the ground. However, note that because of the work done by friction, these energy—work transformations are never perfect. Friction causes the loss of some useful energy.
In the discussions to follow, we will use the approximation that transformations are frictionless. Work was done on the roller coaster to get it to the top of the first rise; at this point, the roller coaster has gravitational potential energy.
It is moving slowly, so it also has a small amount of kinetic energy. As the car descends the first slope, its PE is converted to KE. At the low point much of the original PE has been transformed to KE , and speed is at a maximum. As the car moves up the next slope, some of the KE is transformed back into PE and the car slows down. Help them make the logical leap that, if energy is the ability to do work, it makes sense that it is expressed by the same unit of measurement.
Ask students to name all the forms of energy they can. Ask if this helps them get a feel for the nature of energy. Ask if they have a problem seeing how some forms of energy, such as sunlight, can do work.
Relate this to the origin of a coordinate grid. It is assumed that the speed is constant. Any KE due to increases in delivery speed will be lost when motion stops. Explain that the word potential means that the energy is available but it does not mean that it has to be used or will be used.
This simulation shows how kinetic and potential energy are related, in a scenario similar to the roller coaster. Observe the changes in KE and PE by clicking on the bar graph boxes. Also try the three differently shaped skate parks. Drag the skater to the track to start the animation. This animation shows the transformations between KE and PE and how speed varies in the process. Later we can refer back to the animation to see how friction converts some of the mechanical energy into heat and how total energy is conserved.
On an actual roller coaster, there are many ups and downs, and each of these is accompanied by transitions between kinetic and potential energy. Assume that no energy is lost to friction. At any point in the ride, the total mechanical energy is the same, and it is equal to the energy the car had at the top of the first rise. This is a result of the law of conservation of energy , which says that, in a closed system, total energy is conserved—that is, it is constant.
Using subscripts 1 and 2 to represent initial and final energy, this law is expressed as. Either side equals the total mechanical energy. The phrase in a closed system means we are assuming no energy is lost to the surroundings due to friction and air resistance.
If we are making calculations on dense falling objects, this is a good assumption. For the roller coaster, this assumption introduces some inaccuracy to the calculation. When calculating work or energy, use units of meters for distance, newtons for force, kilograms for mass, and seconds for time.
This will assure that the result is expressed in joules. Compare it to the amount of work it would take to walk to the top of the roller coaster. Ask students why they may feel tired if they had to walk or climb to the top of the roller coaster they have to use energy to exert the force required to move their bodies upwards against the force of gravity. This video discusses conversion of PE to KE and conservation of energy.
The scenario is very similar to the roller coaster and the skate park. It is also a good explanation of the energy changes studied in the snap lab. Before showing the video, review all the equations involving kinetic and potential energy and conservation of energy.
Also be sure the students have a qualitative understanding of the energy transformation taking place. Refer back to the snap lab and the simulation lab. A 10 kg rock falls from a 20 m cliff. What is the kinetic and potential energy when the rock has fallen 10 m? Substitute the known values into the equation and solve for the unknown variables. Alternatively, conservation of energy equation could be solved for v 2 and KE 2 could be calculated.
Note that m could also be eliminated. Note that we can solve many problems involving conversion between KE and PE without knowing the mass of the object in question. This is because kinetic and potential energy are both proportional to the mass of the object. The quantitative relationship between work and the two forms of mechanical energy is expressed by the following equation:. There are a host of other situations in which the only forces doing work are internal or conservative forces.
In such situations, the total mechanical energy of the object is not changed. The external work term cancels from the above equation and mechanical energy is conserved.
The previous equation is simplified to the following form:. In these situations, the sum of the kinetic and potential energy is everywhere the same. As the potential energy is decreased due to the return of a spring to its rest position or a decrease in height above the earth, the kinetic energy is increased due to the object speeding up. We would say that energy is transformed or changes its form from kinetic energy to potential energy or vice versa ; yet the total amount present is conserved - i.
The tendency of an object to conserve its mechanical energy is observed whenever external forces are not doing any overall work. If the influence of friction and air resistance can be ignored or assumed to be negligible and all other external forces are absent or merely not doing work, then the object is often said to conserve its energy. Consider a pendulum bob swinging to and fro on the end of a string. There are only two forces acting upon the pendulum bob. Gravity an internal force acts downward and the tensional force an external force pulls upwards towards the pivot point.
The external force does not do work since at all times it is directed at a degree angle to the motion. As the pendulum bob swings to and fro , its height above the tabletop and in turn its speed is constantly changing. As the height decreases, potential energy is lost; and simultaneously the kinetic energy is gained. Yet at all times, the sum of the potential and kinetic energies of the bob remains constant. The total mechanical energy is 6 J.
There is no loss or gain of mechanical energy, only a transformation from kinetic energy to potential energy and vice versa. This is depicted in the diagram below. As the 2. Use energy equations and the above data to determine the blanks in the above diagram. Click the button to view answers. A common Physics lab involves the analysis of a pendulum in its back and forth motion.
The transformation and conservation of mechanical energy is the focus of the lab. The bob passes through a photogate at location B and another photogate at location C. The speed of the pendulum bob can be determined from the width of the bob and the photogate times. The speed and mass can be used to determine the kinetic energy of the bob at each of the three locations.
The heights of the bob above the tabletop at each of the three locations can be measured and used to determine the potential energy of the bob. The data should reflect that the mechanical energy changes its form as the bob passes from location A to B to C. Yet the total mechanical energy should remain relativity constant. Sample data for such a lab are shown below. The sample data show that the pendulum bob loses potential energy as it swings from the more elevated location at A to the lower location at B and at C.
As this loss of potential energy occurs, the pendulum bob gains kinetic energy. Yet the total mechanical energy remains approximately 0. We would say that total mechanical energy is conserved as the potential energy is transformed into kinetic energy. A roller coaster operates on this same principle of energy transformation.
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