# WORK, ENERGY AND POWER

## WORK

Work is said to be done whenever a force moves a body through a certain distance in the direction of force.  Work done can be defined mathematically as the product of the force and the displacement. It is a scalar quantity & measured in Joules

W = F X d ……………………………………….1.

W = mgh     ……………………………………….2.

If a force is applied on a body at an angle Ø to the horizontal

Work done to move the body on the horizontal plane = Fcos Ø x d ……………………………..3.

Work done to raise the body to an appreciable height = Fcos Ø x d ………………………4.

Examples- A boy of mass 50kg runs up a set of steps of total height 3.0m. Find the work done against gravity

Solution

m = 50kg, h = 3m, g = 10m/s2

Work done = mgh

= 50 x 10 x 3

= 1500 Joules

## Energy

Energy is defined as the ability to do work. It is a scalar quantity & measured in Joules. There are many forms of energy. These include:

1. Mechanical energy
2. Thermal energy
• Chemical energy
1. Electrical energy
2. Nuclear/Atomic Energy
3. Solar/Light energy
• Sound Energy

## Types of Mechanical Energy

Mechanical energy is classified as

• Potential energy
• Kinetic energy

POTENTIAL ENERGY:- is simply “stored energy” i.e. energy possessed by a body by virtue of its states:

P.E = mgh  …………………………………………….5.

KINETIC ENERGY: is the energy possessed by a body by virtue of its motion. Examples area student running a race, wind or air motion, electrical charges in motion, a moving bullet

K.E = ½ mv2  ……………………………………………………6.

Example – An object of mass 5kg is moving at a constant velocity of 15mls. Calculate its kinetic energy.

Solution:

K.E = ½ mv2  = ½ x 5 x 15 x 15 = 562.5 J

Example – Find the potential energy of a boy of mass 10kg standing on a building floor 10m above the ground level. g = 10m/s2

Solution:

P.E =mgh = 10 x 10 x10 =1000 J

## POWER

Power is defined as the rate of doing work or the rate of transfer of energy. It is a scalar quantity & measured in watt

Power = work done

Time                …………………………………………..7

P = (F X d)/t  = F X d/t = FV  ……………………………………8

Example: – : A boy of mass 10kg climbs up 10 steps each of height 0.2m in 20 seconds. Calculate the power of the boy.

Solution

Height climbed = 10 x 0.2 = 2m

Work done = mgh = 10 x 10 x 2 = 200 Joules

POWER = work  =        10 x 10 x 2 = 10watts

Time                     20

EVALUATION

1. Define power.
2. A boy of mass 960g climbs up to 12 steps each of height 20cm in 20 seconds. Calculate the power of the boy.

## WORK DONE IN A FORCE FIELD& ENERGY CONVERSION

Work done in Lifting a Body & Falling Bodies

The magnitude of work done in lifting a body is given by

Work = force x distance = mg x h = mgh

Also, the work done on falling bodies is given by

Work = force x distance = mg x h = mgh

EVALUATION

1. Explain three types of force field.
2. A loaded sack of total mass 100kg falls down from the floor of a lorry 2m high. Calculate the work done by gravity on the load.

## Conservation & Transformation of Energy

Energy can be converted from one form to another in a closed system. The law of conservation of energy states that in an enclosed system, energy can neither be created nor destroyed during transformation. Examples of such conversions include (a) Motor converts electrical to mechanical energy (b) Generator converts mechanical to electrical energy (c) Electric pressing iron convert electrical to heat energy

## World Energy Resources

World energy resources can be classified as

1. Renewable Energy Resources: They are energy that can be replaced as they are used e.g. solar energy, wind energy, water energy & biomass
2. Non-renewable Energy Resources: Energy that cannot be replaced after use e.g. nuclear energy, petroleum & natural gas

EVALUATION

1. State the law of conservation of energy.
2. Differentiate between renewable & non-renewable energy.

## GENERAL EVALUATION

1. When is work said to be done?
2. State the difference between work, energy and power.
3. Differentiate between kinetic and potential energy.
4. State the energy transformation that take place during electricity generation at kanji dam.

## WEEKEND ASSIGNMENT

1. The following are example of force field except (a) electric force (b) magnetic force (c) frictional force (d) gravitational force
2. Electric cell convert ……… to electrical energy (a) nuclear (b) chemical (c) mechanical (d) heat
3. The following are examples of renewable energy except (a) biomass (b) solar (c) wind (d) nuclear
4. A boy of mass 50kg runs up a set of steps of total height 3.0m. Find the work done against  gravity (a) 1200J (b) 1500J (c) 1000J (d) 1300J
5. The SI unit of power is (a) joules (b) kilogram (c) watt (d) pascal
• A bob of a simple pendulum has a mass of 0.02kg. Determine the weight of the bob (a) 0.2w (b) 0.52w (c) 0.25w (d) 2N
• An object of mass 0.5kg has K.E of 25J. calculate the speed of the object (a) 50ms1 (b) 25ms-1  (c) 2.ms-1 (d)10ml-1
• An object of mass 0.5kg has a velocity of 4ms-1 Calculate the K.E (a) 4.0J (b) 40J (c) 0.4J (d) 400J
• Which of the following fundamental quantities is not correctly paired with its unit of measurement? (a) Electricity current – Ampere (b) Amount of substance – kilogram (c) Temperature – Kelvin (c) length – meter
• A diver is 5.2m below the surface of water of density 103 kg/m If the atmospheric pressure is 1.02 x 105 pa. Calculate the pressure on the diver. [g=10mls2 )  (a) 6.02 x 104 pa (b) 1.02 x 105 pa (c) 1.54 x 105 pa (d) 5.20 x 105 pa

## THEORY

• Explain work done.
• A boy of mass 960g climbs up to 12 steps each of height 20cm in 20 seconds. Calculate the power of the boy.
• A loaded sack of total mass 100kg falls down from the floor of a lorry 2m high. Calculate the work done by gravity on the load.
• State the law of conservation of energy.

PRESSURE

DENSITY & RELATIVE DENSITY

VECTOR & SCALAR QUANTIT

FRICTION

MOTION IN NATURE