**Energy**

In the everyday world energy is often the topic of discussion. People talk about the energy used and the cost of energy. Fuel and electricity costs are talked about by many people.

Energy is present in many forms. It exists as mechanical energy, chemical energy, electromagnetic energy and as nuclear energy.

Energy can be changed from one form of energy into another form of energy as long as the principle of the conservation of energy is not violated.

The total amount of energy in a closed system must be a constant and the total energy in the universe is also a constant.

As one form of energy decreases some other form of energy must increase.

A dry cell, commonly but mistakenly called a battery, can convert chemical energy into electrical energy, which can be converted into mechanical energy.

The two main types of energy we will discuss is potential energy and kinetic energy.

We will start our study of energy by a brief study of a concept called work.

**Work**

The common conception of work is incorrect. ** Work** is often considered the same
as a job. People go to work each day but they may not actually do any **work**.

Imagine that you job is to carry boxes of documents from a safe in the
basement, up 10 flights of stairs, to an office where someone will look at these
documents, and that after they have looked at the documents you carry the boxes
back down to the safe and store them for the next day. At the end of the
day, even though you may have been busy all day long and are very tired, the
total amount of your ** work** will be
**zero**.

**Work** is defined as being the
** product** of the component of a
**force** along the
direction of displacement ** times** the magnitude of the displacement.

W = FΔx

If the force is applied at some angle to the direction of travel the equation becomes:

W = (FcosŲ)Δx

where W = **work**, F =
**force**
in the direction of the displacement,
Δx
is the displacement , and Ų is the angle between the line of force and
the direction of the motion.

Older textbooks, and older instructors, may use 's' as the symbol for displacement.

This is commonly stated as **work** equals
**force** times distance.
Remember that the distance refers to the distance moved in the same direction as
the **force**.
When the **force** is as
an angle to the direction of motion a component of the **force**
can be in the direction of the motion.

If you exert a lot of **force**
on an immovable object and the object does not move then you have done no **work**
because nothing was moved.

**Work** is a scalar
quantity.

**Work** can be
positive or negative.

When a baseball bat hits a baseball ** work** is done by the baseball bat on the
baseball. There is an interaction between the baseball bat and the
baseball

Imagine that you pick up a 50 ** kilogram** object off the floor, carry it to the
other side of a large flat room, and place it back on the floor. You have
done no net **work**. Your boss may pay you for doing this even though you
have actually done no **work**
for him, according to the definition of **work**.

**Work Done by a Force that Varies.**

The **work** done by a
**force** that changes
can be determined by a graphing the **force**
in the y direction and the distance in the x direction. The **work**
done will be equal to the area under the curve.

**Work done in Rotary Motion**.

W = FrŲ = TŲ where:

W = **work**

F = **force**** **that
is applied tangentially to the circle

r = **radius** of the
circle

Ų = angle in radians

T = torque

**Work done when stretching or compressing a spring**

Compressing or stretching a spring requires a **force**.
This **force** acting
over a distance causes **work**
to be done on the spring. The more a spring is compressed or stretched the more **force**
is needed and the more **work**
is done.

In the next equation the (1/2) is introduced because the average force is 1/2
the difference of final force minus the initial force. When dealing with the
compression or expansion of a spring the formula for **work**
is as follows:

W = (1/2) (Force) (Distance the spring is stretched or compressed) or

W = (1/2)FΔx
where:

W = **work**

F = **force**** **that
stretches or compresses the spring in **newtons**

Δx
is the distance the spring is stretched or compressed in **meters**

If the **force** needed
is not known but the **spring
constant**, 'k', is known use the following formula.

The **force** to
stretch or compress a spring is found using the following equation:

F = kΔx
where

F = **force** needed
to stretch or compress the spring in **newtons**

k = **spring
constant** measured in N/m

Δx
= distance the **force**
stretches or compresses the spring in **meters**

W = (1/2)(spring constant)( Distance stretched or compressed)^{2} or
simply

W = (1/2)(k)(Δx)^{2}

**Units of Work **

In the **SI
system of measurement** **work**
is measured in **newton-meters**
(n-m) while in the US Customary system of measurement it is measured in
foot-pounds (ft-lb). Other units such as inch-pounds are sometimes used.

The **newton-meter**
is also called a **joule**
which uses the symbol of the upper case 'J'.

**Joule**

The **joule**, named
after **James
Prescott Joule**, is the **SI**
unit of **work** and of **energy**.
The **joule** is the
same a a **newton-meter**.

**Kinetic Energy**

Kinetic Energy is the energy that an object has because of its motion. The
symbol used for kinetic energy is 'KE'. Kinetic energy is also a ** scalar quantity**
with the same unit as **work**, which is the
**newton-meter**, also known as the
**joule**.

KE = (1/2)mv^{2} where:

KE = Kinetic Energy

m = ** mass** of the object

v = ** velocity** of the object

**Work and Kinetic Energy**

W_{net} = KE_{final} -KE_{initial} = ΔKE

The ** work** done by a net force on an object is equal to the change in the
kinetic energy of the object.

**Potential Energy**

Potential energy is the mechanical energy associated with an object because
of its position in a system. Potential energy uses the symbol 'PE' as an
abbreviation. Potential energy is, like **work**
and kinetic energy, a ** scalar
quantity**.

PE = mgh = mgΔy where:

PE = Potential Energy

m = ** mass** of the object

g = ** acceleration due to gravity**

h = height of the object above the reference location.

Δy
= displacement in the vertical direction

Potential energy caused by the objects relative position to the surface of Earth is called gravitational potential energy.

**Gravitational Potential Energy**

Gravitational potential energy associated with the potential energy of an
object based upon its relative position to the surface of the **Earth**.

Gravitational force can cause **work**
to be done.

W_{gravity} = PE_{initial} - PE_{final}

Even though the **acceleration
due to gravity** changes slightly with altitude we normally consider 'g'
to be a constant when working with objects close to the **Earth**.
If a really accurate value is needed the change in the value of 'g' can be taken
into account. We will consider 'g' to remain a constant for our work.

When working problems involving gravitational potential energy you must
select a reference point which is the elevation where you consider the potential
energy to be **cipher**,
or **zero**.

**Reference Levels for Gravitational Potential Energy**

Some elevation must be chosen as the point where the gravitational potential
energy is **zero**. The
surface of the **Earth**
is often chosen as the **zero**
point, but the surface of a floor or desk or table can also be used.
If concerned about objects falling upon your head you might choose the top of
your head to be the point where the gravitational potential energy is **zero**.