Work, Energy and Power

BEHAVIOURAL OBJECTIVES : At the end of the lesson , pupils should be able to

  • define energy
  • mention types of energy
  • explain some phenomena using kinetic theory


Week 2 

Topic: Potential and Kinetic Energy


A stone on the ground does not have any energy so long as it is lying on the ground. The stone cannot be doing any work. However if a stone is placed on a table and it falls off, it can break a lamp on which it falls. The stone here has done some work by virtue of its position. Therefore, when the stone is on the table, it has energy stored up as a result of its position. The type of energy possessed by a body due to its position is called Potential Energy. This energy increases as the height of the table increases and it decreases as it falls towards the ground. When it reaches the ground, it has zero potential energy. Potential energy is the energy that is stored in an object due to its position relative to some zero position. Potential energy, expressed in science as U, is energy that is stored within an object, not in motion but capable of becoming active. An object possesses gravitational potential energy if it is positioned at a height above (or below) the zero height. When you stand at the top of a stairwell you have more potential energy than when you are at the bottom, because the earth can pull you down through the force of gravity, doing work in the process. When you are holding two magnets apart they have more potential energy than when they are close together. If you let them go, they will move toward each other, doing work in the process.

The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters. Notice that gravitational potential energy has the same units as kinetic energy, kg m2 / s2. In fact, all energy has the same units, kg m2 / s2, and is measured using the unit Joule (J).

Examples of Potential Energy:

  • A rock sitting at the edge of a cliff has potential energy. If the rock falls, the potential energy will be converted to kinetic energy.
  • A stretched spring in a pinball machine has elastic potential energy and can move the steel ball when released.
  • When a crane swings a wrecking ball up to a certain height, it gains more potential energy and has the ability to crash through buildings.
  • Tree branches high up in a tree have potential energy because they can fall to the ground.
  • A stick of dynamite has chemical potential energy that would be released when the activation energy from the fuse comes into contact with the chemicals.
  • The food we eat has chemical potential energy because as our body digests it, it provides us with energy for basic metabolism.

Kinetic energy is the energy possessed by a moving body. For example, a moving car, a man running, a falling orange, a fired bullet all possess kinetic energy. This is energy possessed by an object in motion. Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared. Kinetic energy is usually measured in units of Joules (J); one Joule is equal to 1 kg m2 / s2.

Examples of Kinetic Energy

  • Flowing flood water can wash away railway lines and bridges.
  • Water flowing out of a dam can run a turbine to generate electricity.
  • The wind during a storm can uproot big trees.
  • The moving wind can run the blades of a wind mill and can be used for producing electricity or for doing some mechanical work.

Example 1

Calculate the work done if a box is pulled by a person with a force of 150N through a distance of 50m.

Work done = force x distance

Force – 150N

Distance – 50m

Work = 150 x 50 = 7500 joules

Example 2

Suppose a body of mass 1kg is lifted through a height of 1m, how much work is done.

The force of gravity on a mass of 1kg is 10 newtons. Distance moved by the force is 1m.

Work done (force x distance) = 10N x 1m (joules)

Example 3

Suppose a ball of mass m kg falls from a height h m to the ground.  Calculate the potential energy and the kinetic energy of the ball.

Mass of the ball = m kg

Acceleration due to gravity = gm/s2

Distance of fall = h m

Kinetic energy = mgh joules

Suppose the potential energy of the ball was used up at the time it hits the ground, work done = potential energy = mgh joules

Example 4

The kinetic energy of a boat is calculated at 36,000 J. If the boat has a mass of 6,000 kg, with what velocity is it moving?

We identify the information given in the problem:

KE = 36,000 J

mass = 6,000 kg

We now place the information into the kinetic energy formula:

KE = 1/2 mv2

36,000 J = 1/2 (6,000 kg) x (v)2

36,000 J/(1/2 x 6,000 kg) = v2

12 = v2

√12 = v2

3.5 = v

Kinetic Energy to Potential Energy

When a body is thrown up, its velocity gradually decreases as it goes up due to the downward pull of earth. As a result, its kinetic energy decreases and its potential energy increases gradually as the body goes up.
This continues until at a certain height, the kinetic energy of the body becomes zero. At this point, the body has maximum potential energy. So, when a body is thrown up, its kinetic energy decreases and the potential energy increases, because its kinetic energy gradually changes into potential energy.

Practice Questions

  1.  Calculate the kinetic energy of a moving boat at velocity of 3m/s. The mass of the boat is 60kg.
  2. Suppose a body of mass 30kg is lifted through a height of 6m, and the force exerted on the body is 15N, how much work is done?
  3. A man of 50 kg climbs to the top of a building which is 40 m high. What is the potential energy of the man?
  4. The kinetic energy of a car is found to be 40,000 J. What velocity is the car traveling if its mass is 10,000 kg