Work, Power and Efficiency. Fig. 1. Who has done more 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 upto 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.
Remember to measure the displacement in the same direction as the force. Examples: Calculate the work done according to data supplied.
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. Answers.
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.
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.
Answer 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.
Home Experiment  1 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. 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.
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. 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 For the Answers click Physics answer page.

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