7.6 Conservation of Energy

Measure the distance the cup moves after the marble enters it.

The distance the cup moves is determined by the initial marble position on the ruler.

The data can be used to find the coefficients of the cup's spin on the table.

The normal force on the cup is the weight of the cup plus the marble.

The force of gravity and force of gravity do not work because they are not related to the displacement of the cup.
The work is done by friction.
The mass of the marble is needed to calculate the initial energy of the marble.

It is interesting to do an experiment with a steel marble.

A marble is rolled down a ruler.

As you push household objects up and down a ramp, explore forces, energy and work.

To see how the angle of inclination affects the parallel forces on the file cabinet, lower and raise the ramp.

One of the most important physical quantities in nature is energy.

Any process has total energy constant.

It can be transferred from one system to another, but the total remains the same.

Some forms of energy can be transferred from one system to another.

The exploration led to the definition of two major types of energy.
We need to be able to deal with all of the different forms of energy before we can write an equation for the above statement.

We lump all forms of energy into a single group called other energy.

All types of energy and work can be included in this statement.

In previous examples, the equation was not considered because it was constant.

It's important that energy has many forms.

Energy is involved in all processes and is discussed in many contexts.
Many situations are best understood in terms of energy and many problems can be solved by considering energy.

A person eats.

The release of carbon dioxide, water, and energy oxidizes food.
Some of the chemical energy can be converted to thermal energy when the person changes altitude, or to potential energy when the person moves.

A number of forms of energy are not currently discussed.

Many of these will be covered in later chapters.
In batteries, chemical fuel can produce electrical energy.
Light is a very pure form of energy and can be produced by batteries.
The energy we receive from the Sun is stored in most energy sources on Earth.
Nuclear energy is transformed into the energy of sunlight, into electrical energy in power plants, and into the energy of the heat transfer and blast in weapons.
All objects are moving in random motion.
All forms of energy can be converted into one another.

The amount of energy stored, used, or released from various objects is given in Table 7.1.

The variety of types and situations is impressive.

Whenever you deal with energy, you will find the following problem-solving strategies useful.

The strategies help organize and reinforce energy concepts.
The examples presented in this chapter use them.
Identifying physical principles, knowns, and unknowns, checking units, and so on are some of the general problem-solving strategies presented earlier.

Determine the system of interest and figure out how much is given and how much is to be calculated.

A sketch will help.

Do you know if the work done by the forces gives you energy or not?

You can use step 3 or step 4.

If you know the potential energies for the forces that enter into the problem, you can use them to conserve mechanical energy.

If you know the potential energy for only some of the forces, or if there are other forces that do not have a potential energy, then you must conserve energy law in its most general form.

One or more of the terms is a simplification of the problem.

The work done by conservative forces is already included in the terms.

In step 2, you identified the types of work and energy involved.

Eliminate terms before you solve for the unknown.

Solve for the unknown in the usual way.

The answer should be checked to see if it is reasonable.

If you have solved a problem, you should reexamine the forms of work and energy to make sure the equation is correct.
Potential energy at the bottom of a hill should be less than that at the top, and so on.
Check to see if the numerical value is reasonable.
The skateboarder's final speed could be 20 km/h, but not 80 km/h.

All the time, the transformation of energy from one form to another is happening.

Light and chemical energy are converted into thermal and chemical energy through metabolism and photosynthesis.
In a larger example, the chemical energy contained in coal is converted into thermal energy as it burns to turn water into steam in a boiler.

The thermal energy in the steam is converted to mechanical energy when it spins a turbine, which is connected to a generator.

There is an example of energy conversion in a solar cell.

The primary source of solar energy is converted into electrical and mechanical energy.

This solar-power aircraft uses solar cells to convert solar energy into electrical energy.

In an energy conversion process, the output of useful energy or work will be less than the energy input.

Table 7.2 shows the efficiency of mechanical devices.

In a coal-fired power plant, about 40% of the chemical energy in the coal becomes useful electrical energy.