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### Work done.

posted Feb 10, 2015, 9:18 PM by ranmini@charliesresearch.com   [ updated Nov 12, 2017, 11:30 PM by Upali Salpadoru ] Work,  Power
and Efficiency.

Fig. 1. Who has done more work?

There are many ways to measure manual work.

A brick layers work could be measured by the number of bricks he has set.

Jack has laid 100 bricks.
John has laid only 50,

Does that mean Jack has done more work?

Let us just consider two probable inaccuracies.
1. Jack may have used smaller bricks while John fixed  much heavier ones.
2. Jack may have worked at ground level while John had to lift the bricks up-to a considerable height.

In science we must have a method of measurement which can be used to compare work done anywhere.

For any mechanical work to be done, a force is essential.

When a force is applied on a  stationary object, generally there is a movement. A force would cause a change in velocity.

Therefore the product of the force and the resulting displacement of the object gives a good measure of the work done.

The unit for the measurement of work, joule 'J', which has been named after James Prescott Joule, the British scientist 1818 to 1889. Fig,2.  If a force of 1 N is applied over a distance of 1m a joule 'J' of work has been done.

 Work =  Force X Displacement                  Wk = f.d.

Remember to measure the displacement in the same direction as the force.

Examples:-

Calculate the work done according to data supplied. 1. 1. Teddy has pushed a cart weighing 500 N for 5 m. He used a force of 230 N/ 2. A bucket of water weighing 200N has been lifted to a height of 12 meters. 3. A barrel weighing 500 N. has been rolled up an inclined plane 4m. long up to a platform 3 meters high.

 Q.1.      Wk = f.d                 = 230 x 5  =     1150 J .  Weight does not come into the calculation as it is acting in a direction that does not affect horizontal movement. It will certainly increase friction , but we are expected to neglect it.   Q.2.       Work = weight x height.                      = 200 X 12 ……=   2400 JInstead of the weight in newtons, mass was given in kilograms it has to be multiplied by the force og gravity. 9.8 N/kg.Q.3.       Work = weight x height.                      = 500 X 3 =1500 J      The length of the plane cannot be used as the force required in that direction is not given.

• When ever the weight is taken as the force , it is necessary to take the displacement as height.
Measuring Energy
Energy is measured in the same units as work.  In order to get hundred joules of work 100 joules of energy is essential.
• Whenever an object goes up , it gains potential energy

Potential energy  =  mass x g x height.

Potential energy in   =   mgh

J = mgh

'g'  is taken as 9.8  N per kg.   for the gravitational pull of the Earth

Example:- Bob is taking a load of sand . Mass of sand and wheelbarrow is 50 kg.

Man has a mass of 65 kg.

1. 1. Find the work man has to do to get the load to the deck.

2. 2. Find the force he has to use to take the load parallel to the plank.

3. Find the total potential energy man and machine would have gained after ascending to the deck. Take g as 10 ms-2.

1.   Work  = weight X height

Wk= 50 X 3    .............150 J

2.   Work - force x distance.

150  =  F x 4..........   F=   150 / 4     =  37.5  N.

3.   Potential energy =  mass X g  x height.

P.E                 = (50 + 65)  X 10 X 3  J.

= 3450 J.

Power

POWER is the rate of doing work. or rate of changing energy.

Rate means the amount of work that may be done over a certain period of time. Usually the time is taken in seconds.

 Power =Work/Time   P = J /s

Home Experiment - 1
Aim:- To determine the power of  your  arm.
Method:-

Fig.4 An experiment to determine the power of your arm.

Take an  object of known mass in kilograms. If it is 2 kg. The weight of it will be 20 N. Note the time.
Raise the object from the shoulder level to the maximum possible height.

Count the number of times you raise it.

Gravity will work as it comes down. So you can forget about coming down.

You must also measure the height up to which you raise the load.

Use the  formulae given here:-
Work =  m.g.h...........and........Power = m.g.h  / time

A suitable format  to calculate with an example.

Here is an example.

Mary  raised an object weighing 2.0 kg. up to a height of 0.75 m. 25 times.  She took 23 seconds.Find the power of her hand.

Work done  = 2 x 10 x (0.75 x 25)Ioules .

Work done  =  20 x 18.75  Joules
Power        =  375 /  23   Watts
= 16,3 W.

Efficiency

This tells us how good or bad a machine is.
It is calculated  by dividing  work done by a machine by the  energy supplied to the machine . This gives us an idea as to how much energy get wasted.

If we supply 500 J energy to an electric motor, it will not be able to deliver 100 J of mechanical energy. A part of it will get wasted as heat and a part will be used to turn the parts of the machine.
So if it does only  425 J of work the efficiency would be   425 / 500.  That would be  0.85 .
To get the efficiency as a percentage we have to multiply that by 100.  So that will give an efficiency of 85%.
Efficiency = output / input
Efficiency percentage =  (output / input ) x 100.
Use   "g", acceleration due to gravity, as 9.8 ms-2.

Q. 1.0

Jerry at sea level has a mass of 45 Kg. His cycle has a mass of 25 kg. He climbs up a hill for 5000.  M.  reaching a height of 3000 m above sea level in half an hour..

1.1  What is the force the boy is exerting on a cycle when he sits on it.

1.2  What is the support force (Reaction force) the cycle exerts on him?

1.3   What is the amount of work done by him when he reached the top?

1.4   What was the power he had used ?                               (5 x 4 =20 marks)

Q.2.0

A crane lifted a block  having a weight of 2,500 N up to a height of 8 m and lowered it 2 m to the cargo hold of a ship.  The power of the crane was 2.5  kW.

2.1 What is the amount of work done by the crane?

2.2 How much work can the crane perform in 1 second?

2.3 How much time will the crane need to raise the load?

5+5 +10= 20 marks

Q. 3.0

A crate has a weight of 800.N. A man weighing 600.N pushes it up to a height of 3m.along a plane 5m long. The time taken for this was 30 seconds.
Select the answers from the following neglecting friction.

3.1   What is the total work done by the man (+crate) if he had pushed it to the top?

3.2   What is the power he had used?

3.3   What is the useful work done by him?

3.4   What would have been the required force, parallel to the incline, to push the

crate up.?

3.5   A man pulling it using a rope as shown required a force of 512 N.  What could have been the frictional force?

4 x 5 = 20 Marks

Q. 4.0

A water pump has a power output of  2 Horse power.  It has to pump 5000 kg. of water  up to a height of  25 m.                               (1 HP = 746 W.  ,      1kg = 10 N)

4.1  What is the amount of work the pump has to do?

4.2  How much work can the pump perform in one second?

4.3  What is the time it will take to pump 5000 kg of water ?

4.4  If the pump actually took 20 minutes to pump that  amount of water find the percentage efficiency of the pump.

5 x 4 = 20 Marks

Q. 5.0

A boy having a mass of 40  kg.  climbs a stair case  of  12 steps each of 0.2 m high. The time taken was 5  seconds.

5.1   What is the upward force he has to use in climbing?

5.2   What is the amount of work the boy has to do?

5.3   What is the power he would be using?

5.4   What is the Gravitational Potential energy gained by the boy when he reaches the top?

5.5  When the boy jumps out what will be the Kinetic energy on landing?

4 x 5 = 20