# Lesson Notes By Weeks and Term - Junior Secondary School 2

POTENTIAL AND KINETIC ENERGY

TERM: 2nd TERM

SUBJECT: BASIC SCIENCE

CLASS:  JSS 2

REFRENCE

• Precious seed BASIC SCIENCE FOR JUNIOR SECONDARY SCHOOLS BOOK 2

WEEK TWO                                                                                                DATE: ……………..

TOPIC: POTENTIAL AND KINETIC ENERGY

Kinetic energy is energy possessed by a body by virtue of its movement. Potential energy is the energy possessed by a body by virtue of its position or state. While kinetic energy of an object is relative to the state of other objects in its environment, potential energy is completely independent of its environment. Hence the acceleration of an object is not evident in the movement of one object, where other objects in the same environment are also in motion. For example, a bullet whizzing past a person who is standing possesses kinetic energy, but the bullet has no kinetic energy with respect to a train moving alongside.

Definition

The energy of a body or a system with respect to the motion of the body or of the particles in the system.    Potential Energy is the stored energy in an object or system because of its position or configuration.

Relation to environment

Kinetic energy of an object is relative to other moving and stationary objects in its immediate environment. Potential energy is not relative to the environment of an object.

Transferability

Kinetic energy can be transferred from one moving object to another, say, in collisions.

Potential energy cannot be transferred.

Examples, Flowing water, such as when falling from a waterfall. Water at the top of a waterfall, before the precipice. SI Unit is Joule (J)

INTERCONVERSION OF KINETIC AND POTENTIAL ENERGY

The law of conservation of energy states that energy cannot be destroyed but can only be transformed from one form into another. Take a classic example of a simple pendulum. As the pendulum swings the suspended body moves higher and due to its position potential energy increases and reaches a maximum at the top. As the pendulum begins its downward swing, the stored potential energy is converted into kinetic energy.

When a spring is stretched to one side, it exerts a force to the other side so it can come back to its original state. This force is called restoring force and acts to bring objects and systems to their low energy level position. The force required to stretch the spring is stored in the metal as potential energy. When the spring is released, the stored potential energy is converted into kinetic energy by the restoring force.

When any mass is lifted, the gravitational force of the earth (and the restoring force in this case) acts to bring it back down. The energy needed to lift up the mass is stored as potential energy due to its position. As the mass is dropped, stored potential energy is converted to kinetic energy.

Types of Kinetic Energy and Potential Energy

Kinetic energy can be classified into two types, depending on the type of objects:

Translational kinetic energy

Rotational kinetic energy

Rigid non rotating bodies have rectilinear motion. Thus translational kinetic energy is kinetic energy possessed by an object moving in a straight line. Kinetic energy of an object is related to its momentum (product of mass and velocity, p= mv where m is mass and v is velocity). Kinetic energy is related to momentum through the relation E = p2 / 2m and hence translational kinetic energy is calculated as E = ½ mv2. Rigid bodies which rotate along their center of mass possess rotational kinetic energy. Rotational kinetic energy of a rotating body is calculated as the total kinetic energy of its different moving parts. Bodies at rest also have kinetic energy. The atoms and molecules in it are in constant motion. The kinetic energy of such a body is the measure of its temperature.

Potential energy is classified depending on the applicable restoring force.

Gravitational potential energy – potential energy of an object which is associated with gravitational force. For example, when a book is placed on top of a table, energy required to raise the book from the floor and energy possessed by the book due to its elevated position on the table is gravitational potential energy. Here gravity is the restoring force.

Elastic potential energy – energy possessed by an elastic body like the bow and catapult when it is stretched and deformed in one direction is elastic potential energy. The restoring force is elasticity which acts in the opposite direction.

Chemical potential energy – energy related to arrangement of atoms and molecules in a structure is chemical potential energy. Chemical energy possessed by a substance due to the potential it has to undergo a chemical change by taking part in a chemical reaction is chemical potential energy of the substance. When fuel is used, for example, chemical energy stored in fuel is converted to produce heat.

Electrical potential energy – energy possessed by an object by virtue of its electric charge is electrical potential energy. There are two types – electrostatic potential energy and electrodynamic potential energy or magnetic potential energy.

Nuclear potential energy – potential energy possessed by particles (neutrons, protons) inside an atomic nucleus is nuclear potential energy. For example, hydrogen fusion in the sun converts potential energy stored in solar matter into light energy.

Applications

• The roller coaster in an amusement park begins with the conversion of kinetic energy into gravitational potential energy.
• The gravitational potential energy keeps planets in orbit around the sun.
• Projectiles are thrown by a trebuchet making use of gravitational potential energy.
• In spacecrafts, chemical energy is used for takeoff after which the kinetic energy is increased to reach orbital velocity. Kinetic energy gained remains constant while in orbit.
• Kinetic energy given to cue a ball in a game of billiards is transferred to other balls through collisions.

EVALUATION

1. Explain kinetic and potential energy
2. State two application of kinetic and potential energy
3. State the classes of potential energy.

CALCULATING KINETIC AND POTENTIAL ENERGY

For moving objects, we can easily calculate kinetic energy using the formula:

KE = (mass x velocity2)/2 or 1/2 mv2

Although mass and velocity both have great effects on kinetic energy, it is velocity more significantly determines kinetic energy.

Sample Problem

1. What is the kinetic energy of a 45 kg object moving at 13 m/sec?

First we identify the information we are given in the problem:

mass = 45 kg

velocity = 13 m/sec

Next, we place this information into the kinetic energy formula:

KE = 1/2 mv2

KE = 1/2 (45 kg)(13 m/sec)2

Solving the equation gives a kinetic energy value of 3802.5 J

Note: the unit for energy is the same as for work: the Joule (J)

1. Sample Problem

The kinetic energy of a boat is calculated at 52,000 J.  If the boat has a mass of 39,000 kg, with what velocity is it moving?

We identify the information given in the problem:

KE = 52,000 J

mass = 39,000 kg

We now place the information into the kinetic energy formula:

KE = 1/2 mv2

52,000 J = 1/2 (39,000 kg)(v)2

52,000 J/(1/2 x 39,000 kg) = v2

Solving the equation gives a velocity value of 1.63 m/sec

Potential energy is the energy possessed by a body or an object due to its position. Potential energy, on the other hand, is energy of position, not of motion.  The amount of potential energy possessed by an object is proportional to how far it was displaced from its original position. If the displacement occurs vertically, raising an object off of the ground let's say, we term this Gravitational Potential Energy.  We can calculate the gravitational potential energy of an object with this formula:

GPE = weight x height

An increase in the weight of an object or the height to which it is raised will result in an increase in the potential energy the object possesses.  Once the object is dropped, the potential energy begins to decrease due to reduced height, but we also now see an increase in kinetic energy because the velocity is also increasing.

1. Sample Problem

A 37 N object is lifted to a height of 3 meters.  What is the potential energy of this object?

Identify the information given to you in the problem:

weight = 37 N

height = 3 meters

Insert the information into the gravitational potential energy formula:

GPE = weight x height

GPE = 37 N x 3 meters

Solving the problem gives a potential energy value of 111 J.

Evaluation

1. The kinetic energy of a boat is calculated at 50,000 J.  If the boat has a mass of 37,000 kg, with what velocity is it moving?
2. A 38 N object is lifted to a height of 5 meters.  What is the potential energy of this object?

GENERAL EVALUATION

1. Explain kinetic and potential energy
2. State two application of kinetic and potential energy
3. State the classes of potential energy.
4. The kinetic energy of a boat is calculated at 50,000 J.  If the boat has a mass of 37,000 kg, with what velocity is it moving?
5. A 38 N object is lifted to a height of 5 meters.  What is the potential energy of this object?

WEEKEND ASSIGNMENT

1. What is the kinetic energy of a 45 kg object moving at 13 m/sec?  A.  3802.5 J B. 380 J C. 38J D. 382.5 J.
2. The  energy related to arrangement of atoms and molecules in a structure is --------
1. chemical potential energy B.  potential energy C. chemical  energy D. work  potential energy.
1. Potential energy possessed by particles (neutrons, protons) inside an atomic nucleus is A. nuclear potential energy B. nuclear kinetic energy C.  potential energy D. nuclear  energy.
2. The energy of a body or a system with respect to the motion of the body or of the particles in the system is-------A. Potential Energy B. Kinetic  Energy C. Potential system D. Kinematic  Energy.
3. The translational kinetic energy is kinetic energy possessed by an object moving on a
1. straight line B. crooked line C. systemic line D. steam line

THEORY

1. State two application of kinetic and potential energy
2. State the classes of potential energy.