Student:
Mr. Khalilian & Ms. Townsend
Physics, _________________
Due Date:
HW4.2 Energy Reading
Types of Energy
Read and take notes.i After the reading, use your notes to answer the questions. If you need to, go back to the
reading. But add whatever you used from the reading to answer the question into your notes.
Potential Energy
An object can store energy as the result of its position. For example, the heavy ball of a demolition
machine is storing energy when it is held at an elevated position. This stored energy of position is referred to as
potential energy. Similarly, a drawn bow is able to store energy as the result of its position. When assuming its
usual position (i.e., when not drawn), there is no energy stored in the bow. Yet when its position is altered from
its usual equilibrium position, the bow is able to store energy by virtue of its position. This stored energy of
position is referred to as potential energy. Potential energy is the stored energy of position possessed by an
object.
Gravitational Potential Energy
The two examples above illustrate the two forms of potential energy
to be discussed in this course - gravitational potential energy and elastic
potential energy. Gravitational potential energy is the energy stored in an
object as the result of its vertical position or height. The energy is stored as
the result of the gravitational attraction of the Earth for the object. The gravitational potential energy of the
massive ball of a demolition machine is dependent on two variables - the mass of the ball and the height to
which it is raised. There is a direct relation between gravitational potential energy and the mass of an object.
More massive objects have greater gravitational potential energy. There is also a direct relation between
gravitational potential energy and the height of an object. The higher that an object is elevated, the greater the
gravitational potential energy. These relationships are expressed by the following equation:
𝑚
𝐺𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 = 𝑚𝑎𝑠𝑠 𝑥 (9.81 2 ) 𝑥 ℎ𝑒𝑖𝑔ℎ𝑡
𝑠
𝐺𝑃𝐸 = 𝑚𝑔ℎ
In the above equation, m represents the mass of the object, h represents the height of the object and g
represents the gravitational field strength (9.8 m/s2 on Earth) – also known as the
acceleration of gravity.
To determine the gravitational potential energy of an object, a zero height
position must first be arbitrarily assigned. Typically, the ground is considered to
be a position of zero height. But this is merely an arbitrarily assigned position
that most people agree upon. Since many of our labs are done on tabletops, it is
often customary to assign the tabletop to be the zero height position. Again this
is merely arbitrary. If the tabletop is the zero position, then the potential energy
of an object is based upon its height relative to the tabletop. For example, a pendulum bob swinging to and from
above the tabletop has a potential energy that can be measured based on its height above the tabletop. By
measuring the mass of the bob and the height of the bob above the tabletop, the potential energy of the bob can
be determined.
Aim/Purpose of this assignment: To understand the types of energy.
1
Student:
Mr. Khalilian & Ms. Townsend
Physics, _________________
Due Date:
HW4.2 Energy Reading
Types of Energy
Since the gravitational potential energy of an object is directly proportional to its height above the zero
position, a doubling of the height will result in a doubling of the gravitational potential energy. A tripling of the
height will result in a tripling of the gravitational potential energy.
Elastic Potential Energy
The second form of potential energy that we will discuss is elastic
potential energy. Elastic potential energy is the energy stored in elastic
materials as the result of their stretching or compressing. Elastic potential
energy can be stored in rubber bands, bungee cords, trampolines, springs, an
arrow drawn into a bow, etc. The amount of elastic potential energy stored
in such a device is related to the amount of stretch of the device - the more
stretch, the more stored energy.
Springs are a special instance of a device that can store elastic potential energy due to either
compression or stretching. A force is required to compress a spring; the more compression there is, the more
force that is required to compress it further. If a spring is not stretched or compressed, then there is no elastic
potential energy stored in it. The spring is said to be at its equilibrium position. The equilibrium position is the
position that the spring naturally assumes when there is no force applied to it. In terms of potential energy, the
equilibrium position could be called the zero-potential energy position. There is a special equation for springs
that relates the amount of elastic potential energy to the amount of stretch (or compression) and the spring
constant. The equation is
1
𝑠𝑝𝑟𝑖𝑛𝑔 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 = 𝑥 𝑠𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑥 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛2
2
1
𝑆𝑃𝐸 = 𝑘𝑥 2
2
where k = spring constant
x = amount of compression (relative to equilibrium position)
To summarize, potential energy is the energy that is stored in an object due to its position relative to
some zero position. An object possesses gravitational potential energy if it is positioned at a height above (or
below) the zero height. An object possesses elastic potential energy if it is at a position on an elastic medium
other than the equilibrium position.
Kinetic Energy
Kinetic energy is the energy of motion. An object that has motion - whether it is vertical or horizontal motion has kinetic energy. There are many forms of kinetic energy - vibrational (the energy due to vibrational motion),
rotational (the energy due to rotational motion), and translational (the energy due to motion from one location to
another). To keep matters simple, we will focus upon translational kinetic energy. The amount of translational
kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) that an object
has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following
equation is used to represent the kinetic energy (KE) of an object.
1
𝐾𝑖𝑛𝑒𝑡𝑖𝑐 𝐸𝑛𝑒𝑟𝑔𝑦 = 𝑥 𝑚𝑎𝑠𝑠 𝑥 (𝑠𝑝𝑒𝑒𝑑)2
2
1
𝐾𝐸 = 𝑚𝑣 2
2
where m = mass of object, v = speed of object
This equation reveals that the kinetic energy of an object is directly proportional to the square of its
speed. That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four. For a
threefold increase in speed, the kinetic energy will increase by a factor of nine. And for a fourfold increase in
speed, the kinetic energy will increase by a factor of sixteen. The kinetic energy is dependent upon the square of
Aim/Purpose of this assignment: To understand the types of energy.
2
Student:
Mr. Khalilian & Ms. Townsend
Physics, _________________
Due Date:
HW4.2 Energy Reading
Types of Energy
the speed. As it is often said, an equation is not merely a recipe for algebraic problem solving, but also a guide
to thinking about the relationship between quantities.
Kinetic energy is a scalar quantity; it does not have a direction. Unlike velocity, acceleration, force, and
momentum, the kinetic energy of an object is completely described by magnitude alone.
For all types of energy, the standard metric unit of measurement for kinetic energy is the Joule. As might
be implied by the above equation, 1 Joule is equivalent to 1 kg*(m/s)2.
1 Joule = 1 kg • m2/s2
The Total Mechanical Energy
The mechanical energy of an object can be the result of its motion (i.e., kinetic energy) and/or the result
of its stored energy of position (i.e., potential energy), or both (if an object is both at a height and moving). The
total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy. This sum is
simply referred to as the total mechanical energy (abbreviated TME). As discussed earlier, there are two forms
of potential energy discussed in our course - gravitational potential energy and elastic potential energy. Given
this fact, the total mechanical energy of an object can be calculated by using:
𝑇𝑀𝐸 = 𝐺𝑃𝐸 + 𝑆𝑃𝐸 + 𝐾𝐸
If one of the forms is not present (for instance, if there is no spring), than that particular form of energy
is just 0 J. The diagram below depicts the motion of Li Ping Phar (esteemed Chinese ski jumper) as she glides
down the hill and makes one of her record-setting jumps.
The total mechanical energy of Li Ping Phar is the sum of the potential and kinetic energies. The two
forms of energy sum up to 50 000 Joules. Notice also that the total mechanical energy of Li Ping Phar is a
constant value throughout her motion. For now, merely remember that total mechanical energy is the energy
possessed by an object due to either its motion or its stored energy of position. The total amount of mechanical
energy is merely the sum of these two forms of energy.
Aim/Purpose of this assignment: To understand the types of energy.
3
Student:
Mr. Khalilian & Ms. Townsend
Physics, _________________
Due Date:
HW4.2 Energy Reading
Types of Energy
Questions to be answered on a sheet of notebook paper.
1. Define the following terms:
a. Potential energy
b. Gravitational potential energy
c. Spring potential energy
d. Kinetic energy
e. Total mechanical energy
2. Give the abbreviated equations to calculate the following quantities and what the variables stand for (the
first one has been done as an example, in italics):
a. Gravitational potential energy
GPE = mgh
GPE = gravitational potential energy
m = mass
g = 9.81 m/s2 (gravitational field strength)
h = height
b. Spring potential energy
c. Kinetic energy
d. Total mechanical energy
3. What is the unit for all types of energy?
4. Solve the following problems:
a. A 27 kg child sits at the top of a slide that is 1.8 meters above the ground. What type of potential
energy is this? What is the potential energy of the child?
b. Determine the potential energy of a 0.30 kg arrow that is pulled back 0.25 m in a bow. What type
of potential energy is this?
c. Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.
d. Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of
12 000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed?
i
Readings taken from www.physicsclassroom.com. The answers to 4c and 4d are also available there, as well as some
demonstrations.
Aim/Purpose of this assignment: To understand the types of energy.
4