WORK, ENERGY AND POWER.

Specific objectives.

• Define work, energy and power and state their SI units.
• Define energy transformation.
• Explain the law of conservation of energy.
• Solve numerical problems involving work, energy and power.

                                    Work.

• Is said to be done only when a force produces a displacement of a body.
• Is said to be done when an applied force causes a body or an object to move in its direction.

                        SI units = Joules

• It depends on;

1. The force applied.
2. The displacement of the body.

Work = force   x   displacement

        = f    x     d              N/m

Types of work.

Positive work.

• Work done is said to be positive if the displacement is in the direction of force.

Negative work.

• Work done is negative if the displacement is opposite to the direction of force e.g. when a body is lifted, work done by gravitational force is negative as displacement is against the direction of force of gravity.

Zero work.

• Work done is zero;

1. When there is no displacement on the body e.g. pushing a stationary object or a wall.
2. When a body is suspended. The weight of the body acting downwards balances with the tension of the spring acting downwards.

• When force is perpendicular to the displacement. When a body slides over a frictional surface, the only force acting is the weight of a body and is perpendicular to displacement.

1. When a body is moving in circles.

Energy.

• Is the capacity of doing work or overcoming resistance.
• Is the ability to do work.

                        SI units = joules(J)

                        Sources of energy.

1. The sun – main source.
2. Wind – air in motion.
3. Fuel – wood, petroleum, natural gas, coal.
4. Geothermal – Heat from the earth that heat water to produce steam that turn turbines in geothermal power stations.
5. High dams and waterfalls – Used in hydroelectric power stations.
6. Ocean – tides and waves.
7. Nuclear energy – Atomic energy used to produce electricity.

                        Renewable and non- renewable energy sources.

Renewable energy.

• Is that which is supplied by processes in the environment that can be recycled or re-used over and over again. The supplies are inexhaustible e.g

                        Solar                geothermal     wave or tides  wind

Non – renewable.

• Is energy supplied by processes that are exhaustible. The materials used cannot be retrieved e.g.

                        Firewood         coal                 petroleum                   nuclear energy                        biogas              alcohol

                                    Forms of energy.

• Mechanical energy.
• There are two types.

1. Potential energy.

• There are three types

1. Gravitational potential energy (g.p.e). Energy possessed by a body due to its relative position or state from the center of the earth

g.p.e = mgh

1. b) Elastic potential energy(e.p.e). Is the energy possessed by an elastic body or a compressed spring.

                                    e.p.e = ½ fe

1. c) Electric potential energy(p.d). Is energy per charge provided by a cell to make the electric charges to move across two

points in an electric circuit

1. Kinetic energy (k.e)

• Is energy possessed by objects in motion

                                    k.e = ½ mv²

2) Heat energy

• Form of energy that flows from one region to another due to temperature difference.

3) Chemical energy.

• Is the energy contained in chemical substances and can be converted to heat energy by the process of oxidation.

4) Light energy.

5) Sound energy.

                                    Conservation of energy.

• The law of conservation of energy states that energy can neither be created nor destroyed but can change from one form to another.
• It states that the sun of p.e and k.e is constant.

                                    Transformation of energy.

• Energy can be converted from one form to another.
• Any device that facilitates energy transformation is called a transducer.

                                    Power.

• Is the rate of doing work.
• Is the rate at which enerht is converted from one form to another.

            Power=    = J/s

            SI units = watts (W)

                                    Devices.

• A device is that which help to convert energy from one form to another.
• There are electrical and mechanical devices.
• Electrical devices are;

1. A dynamo or generator where input Is mechanical and output are electrical energy.
2. An electric motor. Converts electrical energy to mechanical energy, that is, its output is mechanical energy.
3. Transformer where both input and output are electrical energy.

Mechanical devices.

• These are devices which both input and output are mechanical energy e.g. machine.

                                    Machine.

• A machine is a device that enables us to perform work more easily, quickly and more conveniently.
• There are different types of machines;

1. Simple levers.
2. Pulley system.

• Inclined planes.

1. Screw jack.
2. Gear system
3. Hydraulic machines

• Wheel and axle

                                       Terms used.

            Effort (E)

• The force applied to the machine.

              Load (l)

• The force exerted by a machine.
• It is that which the machine lift or move.

              Mechanical advantage (M.A)

• The ratio in which the machine increases the force
• The ratio of force to effort.

                        M.A =  

• It depends on friction.

                 Velocity ratio (V.R)

• The ratio of effort moved distance to the load moved distance.
• It does not depend on friction but the geometry of the machine

                        V.R =

             Efficiency of the machine (E)

• The ratio of power output to power input expressed as a percentage.
• The ratio of mechanical advantage to velocity ratio expressed as a percentage.

                            E =  x 100

                             E =  x 100

                               = X 100

• Efficiency of a machine is always less than 100% as there are no perfect machines.
• Some energy is lost as heat energy and sound are overcoming frictional force.

                                           Levers.

• Are simple machines that produce large force from smaller forces.
• They operate under the principal of point i.e. the moment of force about a point is the product of the force and the perpendicular distance of its line of action from that point.
• When a lever is balanced and the effort is just about to move the load

                                            Effort  x   effort distance =   x load distance

                                             =

                                   M.A =  = This is the principal of levers.

• This means that the M.A of levers depends on the relative distance of the effort and the load of the pivot.
• There are three classes of lever.

1. 1^st class order.

• The fulcrum/pivot is between the effort and load.
• The effort arm is equal or greater than the load arm.
• A is greater or equal to 1.
• Example include; scissors         lever balance                  hammer      top opener

1. 2^nd class order.

• The load is between the pivot and effort.
• The effort arm is greater than the load arm.
• A is greater than 1.
• Examples include; Wheelbarrow Nutcracker

1. 3^rd class order.

• Effort is between load and pivot.
• The effort arm is less than the load arm.
• A is less than 1.
• Examples include; forearm forceps            fishing rod            spade
• To increase M.A efficiency of simple levers, the load is placed near the fulcrum.

                                         Pulley system.

• Used to change the direction of force (effort).
• It is easies and usually more convenient to raise a heavy load by pulling downwards than by lifting it.
• Produce a large force from a smaller force.
• There are two types of pulleys.

1. Single pulley.
2. Block and tackle pulley system.

Single pulley system.

• There are of two types.

1. Single fixed pulley.

• The effort applied is equal to the load moved. M.A is equal to 1.
• The V.R is equal to 1 as the distance load move equal to effort distance.
• It helps to raise the load by pulling downwards.

1. Single movable pulley.

• Has low efficiency since the M.A is less than the V.R. M.A is less than 1 and V.R is 2.
• The effort is much greater than the load for it has to lift the movable pulley and overcome frictional force.

                                Block and tackle pulley system.

• Uses both fixed and movable pulleys.
• There are two pulley blocks, a fixed upper block and a movable lower block to which the load is attached.
• A single string of rope is used which passes round each pulley in turn.
• One end is tied to one of the pulley block while the other end is attached to the effort or where the effort is applied.

                               V.R = number of pulleys on a block and tackle system.

• Its equal to the number of strings supporting the load or lower movable block e.g. if there are two strings supporting the load and it has to move one meter, the string will move one meter hence two meters in total, V.R= 2

                                      Application of pulleys.

1. Convey belts.
2. Sewing machines.

                                      Efficiency of a single string pulley system.

• If a graph of M.A is plotted against load and efficiency against load, they give a curve.

• As the load increases, the M.A and efficiency increases. This is because at high load, the mass of the moving puller and the frictional forces are very small compared with the load.
• The efficiency is always less than 100% because extra effort is required to;

1. Lift the weight of the lower pulley block and strings.
2. Overcome the friction between the strings and the rims of the pulley.

• Friction reduces M.A but has no effect on the V.R.

                                      Inclined plane.

• A slope which allows a load to be raised more gradually by using a smaller effort than if it were lifted vertically upwards.

Distance moved by the effort = l

Distance moved by the load = h

V.R =       =

Sin =

= = V.R

V.R =

• The efficiency of an inclined plane decreases with increase in the angle of inclination of the plane.

                                      Screw jack.

• Used to raise vehicles off the ground for the purpose of repair.

• When the screw moves or turns one revolution, the effort moves round a circle of radius r equal to the circumference.

                   C = 2r

• The load moves up a distance equal to the pitch of the screw P which is the distance between two consecutive threads or turns.

                   V.R = =

• The velocity ratio is very high since the pitch is very small as compared to the length of the handle.
• The efficiency is very low, less than 50% because the frictional force is very high so that the screw does not slide back when left.

                                      Gear system.

• A gear is a wheel which can rotate about its center.
• It has equally spaced teeth or cogs around it.
• The wheel in which the effort is applied is called a driver or effort gear while the wheel to which the load is applied is called the driven wheel or load gear.
• If the driving wheel has “n” teeth and the driven wheel has “N” teeth, then when the driving wheel makes one revolution, the driven wheel makes

             V.R =

             V.R = 1 ÷= 1 x

V.R = =

V.R = =

                              Hydraulic machines.

• Machine used to obtain a large force from a small force with the help of a liquid.
• It operates on the principal that liquid transmit pressure equally in all directions.
• It consists of ;

1. Tight fitting piston P moving in a narrow cylinder X.
2. Tight fitting piston Q moving in a wide cylinder Y.
3. A liquid, oil or water moving in both cylinders.

Pressure in cylinder X due P = P₁ =

Pressure in cylinder Y = P₂ =

Since the liquid cannot be compressed and liquid transmit pressure equally in all directions, then P₁ = P₂

                   Or     =

Or  =                      i.e.  = M.A

                  Velocity ratio (V.R).

• Let the effort piston move down length L₁
• The volume of the liquid displaced V₁ = A₁L₁
• The load piston moves up a distance L₂
• The volume increases in large cylinder V₂ = A₂L₂
• Since the liquid is incompressible, V₁ = V₂ or A₁L₁ = A₂L₂

 =           =

V.R =  =

• The V.R depends on the area of the sides of the piston.

                                            Wheel and axle.

• Helps to use a small effort to overcome a large force (load).
• It consists of a wheel where the effort is applied and an axle where the load is applied.

M.A =  , which is always greater than for heavy load.

V.R

• Let the wheel and axle make one complete revolution.
• The effort moves down a distance equal to the circumference of the axle
• The rope round the axle moves up a distance equal to the circumference of the axle =

                  V.R =    =

                   =    =

• They are used in

1. Steering wheels.
2. Wells.
3. Windlass.
4. Screw driver.