Using mechanical energy for daily

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1 unit 3 Using mechanical energy for daily activities Physics Chapter 3 Using mechanical energy for daily activities Competency Uses mechanical energy for day-to-day activities Competency level 3.1 Investigates how mechanical energy is used to do work 3. Estimates the value of mechanical energy 3.3 Investigates various methods to make work easy Subject content ² Work ² SI unit to measure work (J) ² Mechanical energy ² Potential energy ² Kinetic energy ² Law of conservation of energy ² Power ² SI unit of power (W) ² Relationship between energy and power ² kw h as a unit of energy ² Potential energy, E P = mgh ² Kinetic energy E k = ½ mv ² Calculations related to energy ² Nature of conservation of energy ² Simple machines and engines ² Mechanical advantage ² Velocity ratio ² Efficiency For free distribution 45

2 Physics 3.1 How mechanical energy is used to do work 1 m work done 1 J 1 N Energy means the ability to do work. Energy is spent when work is done. There are various forms of energy such as, Mechanical energy Heat energy Chemical energy Magnetic energy Electrical energy Sound energy Light energy Fig : 3.1 An instance where work of one joule is done. Several instances where mechanical energy is used to do work, are considered here. It is necessary to move a force along a distance for a work to be done. When a force of 1 newton (1 N) is applied along a distance of 1 meters (1 m) then the work done is known as 1 joule (1 J) Work done when a force of 1 N is acting along a distance of 1 m = 1 J Work done when a force of 5 N is acting along a distance of 1 m = 5 J Work done when a force of 5 N is acting along a distance of m = (5 x ) = 10 J Work done = Force Displacement of the point of action of force (towards the direction of force) J = 1 kj (kilo joule) J = 1 MJ (mega joule) Knowledge check ² Fill in the blanks of the following table Force applied Distance of the motion of the point of action of force work done 0 N 6 m m 00 J 40 N 50 cm N... 4 J 10 N 0.4 m For free distribution

3 Fig : 3. mass 1 kg 10 N weight weight of a mass of 1 kg is 10 N. 1 kg g = 10 m s - 10 N unit 3 Using mechanical energy for daily activities ² Example What is the amount of work done, when a mass of 8 kg is lifted vertically to a height of 5 m? To solve this problem, the force necessary to lift the object vertically up should be found first. Weight of a mass of 1 kg = 10 N Therefore a force of 80 N is necessary to lift an object with a mass of 8 kg Force applied = 80 N Distance of the motion of object towards the direction of force (height) = 5 m Work done = Force Distance 80 N 5 m 400 J 10 N Here an amount of 400 J of energy is transmitted into the object. Fig : 3.3 Force exerted to lift a mass of 1 kg. Knowledge check 1. Find the amount of work done, when an object of a mass of 1 kg is lifted to a height of 3 m. Mass of a packet of tea is 100 g. Find the amount of work done, when it is lifted to a height of 1.5 m. 3. When an object of a mass of 5 kg is lifted to a certain height, the work done is 00 J. what is that height? 4. The mass of a man is 50 kg. What is the amount of work done, when he climbs to a vertical height of 6 m? 5. Calculate the amount of work done, when a mass of m kg is lifted to a height of h m. [Acceleration due to gravity (g) = 10 m s - ] For free distribution 47

4 Physics Mechanical energy Mechanical energy is of two types. 1. Potential energy. Kinetic energy Potential Energy Potential energy of an object is the energy stored in the object, due to its height of position or the change of its natural shape. Think of a piece of stone positioned on a hill top. If it falls down hill, work would be done. That is because the potential energy stored in it is converted to another form of energy (Fig : 3.4) Assume that the mass of a piece of stone on a hill top of 00 m high is 8 kg. Fig : 3.4 Energy stored in a stone positioned on a hill top is gravitational potential energy Weight of the stone Work done when it falls 00 m down Therefore the energy stored in the piece of stone (potential energy) = 8 kg «10 m s - = 80 N = 80 N «00 m = J = J This value is obtained by 8 kg «10 m s - «00 m Mass (m) acceleration due to gravity (g) height(h) Fig : 3.5 Energy stored in a stretched spring is elastic potential energy Energy stored in an object due its position of height is known as gravitational potential energy. Gravitational potential energy } m «g «h When a spring is stretched and released, a work is done. When a rubber band is stretched and released, again work is done. That is because of the storage of energy in stretched springs and stretched rubber bands. Energy stored in such objects is elastic potential energy. 48 For free distribution

5 unit 3 Using mechanical energy for daily activities There is a coconut with a mass of.5 kg at the height of 0 m on a coconut tree. Calculate the potential energy stored in the coconut. (g = 10 m s - ) Mass of the coconut =.5 kg Height to the coconut = 0 m Potential energy stored in it = mgh =.5 kg x 10 m s - x 0 m = 500 J Kinetic energy Kinetic energy is the energy stored in a moving object because of its motion. Given below are some things where kinetic energy is stored. 1. Blowing wind 3. Motor vehicle in motion. Flowing water 4. Flying bird If two objects of different masses are moving in the same speed, more energy is stored in the object with higher mass. On the other hand, if two object of the same mass are moving in different speeds, more energy is stored in the object of higher speed. Therefore it is clear there are two factors affecting the kinetic energy of an object. 1. Mass of the object. Speed of the object Kinetic energy is denoted by E k Assume an object of mass m, zero initial speed and speed v after time t. v t Acceleration of a moving object, a = Force acting on the moving object, F = ma = m «Mean (average) speed = 0 + v Distance Moved = mean velocity «time v = «t Work done = Force «distance moved mv = ^ & «^ vt t & 1 Kinetic energy of the object mv Kinetic energy stored in an object } = E of mass m, moving in velocity v k = 1 mv v t = v For free distribution 49

6 Physics Calculations related to kinetic energy Example 1 What is the kinetic energy contained in an object of the mass of kg, moving in a velocity of 6 m s -1? Kinetic energy, 1 E k = mv 1 = «kg «(6 m s 1 ) = 1 «kg «36 m s = 36 J Example What is the kinetic energy stored in an object of 5 kg, moving in a velocity of 10 m s -1? Kinetic energy, E k = 1 mv = 1 «5 kg «(10 m s 1 ) = 1 «5 kg «100 m s = 50 J 1 J = 1 kg m s - Law of conservation of energy This law states that energy could neither be created nor be destroyed. Only what could be done is the conversion from one energy form to another energy form. This happens when work is done. Do you know? Power Power is the rate of work done. The amount of work done in a given period of time is known, power could be calculated by dividing the amount of work done by time. Power = Work done Time taken Let amount of work done in 10 seconds is 600 J; Fig : 3.6 James Watt. Unit of measuring power is named after this scientist, who is also the inventor of steam engine. 600 J Power = = 60 J s 1 10 s J s 1 is Watt (W). Unit of measuring power is Watt (W) Think of a machine with a power of 500 W. Work done by this machine during one second is 500 J. If the power of a machine is 5 kw, it is equal to W. It can do an amount of work of J per second. 50 For free distribution

7 unit 3 Using mechanical energy for daily activities Think of a machine of 1 kw. The power of it is 1000 W W is a power of 1000 J s -1. When this machine works for 1 hour, the amount of energy spent is known as 1 kilo watt hour (1 kw h) 1 kw = 1 000W = J s -1 Energy spent in 1 s = J 1 h = s Energy spent in s = J s s = J 1kW h = J Therefore kilo watt hour (kw h) is used as a unit of measuring large amount of energy. Example Power of a machine is 1.5 kw. If this machine worked continuously for 0 h in that power, how much energy was spent? Amount of energy spent = Power «Time = 1.5 kw x 0 h = 30 kw h Methods of making Jobs easy Simple machines and engines Simple machines and engines make work easy, and engines do work more speedily, Simple machines Simple machine is a set - up in which a in one point is supressed by a force () applied to another point. Given below are some commonly used simple machines. ² Lever ² Inclined plane (ramp) ² Pulley ² Wheel and axle Fig : 3.7 Lever Fig : 3.8 Inclined plane For free distribution 51

8 Physics Fig : 3.9 Pulley In every machine, is applied to one point and it is transmitted to the acting on another point of the machine. How we can making work easy by machines? 1' Work that needs a large could be done by applying smaller on the machine. ' Direction of applying force could be changed. 3' Rate of doing work could be increased. Mechanical advantage Work should be applied on the machine for a work to be done by the machine. For this, a force should be applied on the machine. That force is called the. The force suppressed by the machine by applying the is called. Mechanical advantage of a machine is the ratio of the suppressed (L) to the applied (E) Fig : 3.10 Wheel and axel Mechanical Advantage = Load Effort = L E Velocity ratio Ratio of the velocity of motion of to that of is the velocity ratio. But both and moves in the same time. Therefore velocity ratio could be obtained by dividing the distance of the movement of by that of. Velocity ratio = Distance moved by Distance moved by. Efficiency We have to do work on a machine for the work to be done by the machine. True or the effective work done by the machine is reffered to as work output. To find the amount of work output, should be multiplied by the distance moved by. 5 For free distribution

9 unit 3 Using mechanical energy for daily activities Effective work or the work output of a machine = Load distance moved by If is 600 N and distance moved by is 0 cm. 0 Work output = 600 N «m = 10 J 100 That amount of work is done by the machine because of the work done by the on the machine. Work done on the machine (work input) = Effort Distance moved by If the exerted on the machine, in the above instance is 00 N and the distance moved by the is 80 cm; Work done on the machine or work input } = ^00 N «80$100 m&} 160 J Here work done on the machine or the work in-put is 160 J and work done by the machine or the work out-put is 10 J. Work of 40 J is wasted. That amount of work is used to give energy to suppress resistant forces like friction. Hence that energy is used to generate heat or vibrations. Heat and vibrations of machines, when they are at work are due to the evergy wasted. Always the work output of a machine in practice is less than the work input of it. In the above example; Work input Work output = 160 J = 10 J Then what will be the work output, if work input is 100 J? It will be 10 «100] = 75] 160 This result is known as efficiency of the machine. It is always given as a percentage. Efficiency = Work output 100% Work Input Efficiency = distance moved by 100% distance moved by = distance moved by distance moved by 100% = mechanical advantage velocity ratio 100% Efficiency = mechanical advantage velocity ratio 100% For free distribution 53

10 Physics Levers arm A lever is a bar which can be moved freely round a pivot fulcrum arm Fig : 3.11 Lever as a simple machine Memorise the instance that a crow bar or any other bar is used to lift a stone. Here, one end of the crow bar is kept under the stone. Something like a small log is kept under the bar, close to the stone as a support. A force is applied to the far end of the bar to lift the stone (see Fig : 3.11) All the points of the bar, other than the point that touches the supportive piece of log, moves. Here, crow bar acts as a lever. Motionless point of the lever is called fulcrum. Force suppressed by the lever (weight of the stone) is the. Force applied on the lever is the. Distance from the point of action of to the fulcrum is length of arm. Distance from the point of action of to the fulcrum is the length of arm. If the arm is longer than the arm of a lever, more could be lifted by applying less. There are three types (or orders) of levers according to the relative positions of, and fulcrum. First order levers Here fulcrum is positioned in-between the and. Pair of scissors, pair of pliers, and see-saw are some examples for first order levers. (Fig : 3.1) Load Fulcrum Effort See-Saw Pair or scissors Fig : 3.1 First order levers Pair of pliers 54 For free distribution

11 Fulcrum Load Effort unit 3 Using mechanical energy for daily activities Second order levers In second order levers, fulcrum is at one end. Effort is at the other end. Load is in-between these two. Wheel barrow and Nut cracker are some examples. Nut cracker Fig : 3.13 order levers. Second Third order levers Wheel barrow When fulcrum is at one end, is at the other end and the is applied in-between those two; such levers are called third order levers. Forcep, broom and fishing rod are some examples. Fulcrum Fig : 3.14 Effort Third order levers Load forcep Fishing rod Using ramp to weights Wedge Screw nail Fig : 3.15 Inclined plane Inclined plane Ramps or inclined planes are also used to ease work. You may have seen how barrels of oil are ed into a truck. A large force should be applied to lift them directly. But when an inclined plane is used, the force applied could be reduced. Given below are some examples where inclined planes are seen. 1' Screw jack 5' Wedge ' Screw nail 6' Stair case 3' Ladder 7' Cutting edge of a knife 4' Chisel 8' Winding roads in mountains. For free distribution 55

12 Physics Solved Example ² An inclined plane of the length of 4m, used to elevate an object with a mass of 150 kg to a height of 1m is shown in the diagram here. Force applied to draw the object along the inclined plane () is 500 N. 4 m 1500 N 500 N 1 m ^I& What is the weight of the object ()? (g=10 m s - ) ^II& What is the mechanical advantage of this inclined plane? ^III& What is its velocity ratio? ^IV& Calculate the efficiency of the inclined plane. ^I& Mass of object } 150 kg Its weight } 150 kg «10 m s - } 1500 N ^II& Mechanical advantage } 1500 N 500 N } 3 ^III& Velocity ratio } } Distance moved by Distance moved by 4 m 1 m } 4 ^IV& Efficiency of the inclined plane } Mechanical advantage «100% Velocity ratio 3 } 4 «100% } 75% } Fig : 3.16 Pulley as a simple machine Pulleys Pulley used to draw water from wells is an example for this. It is a non- moving single pulley. Non-moving single pulleys as well as blocks of pulleys (or sets of pulleys) are used to ease work. Let us consider non-moving single pulley first. The pulley is fixed to horizontal bar. Therefore its axis is not moving. Load is acting at one end of the string sent round the pulley. and is applied to the other end. As the distance moved by the and the distance moved by are equal, the 56 For free distribution

13 unit 3 Using mechanical energy for daily activities velocity ratio of single pulley is one (Fig : 3.16) But cannot be lifted up by applying an equal because of the friction of the pulley. Therefore it is necessary to apply an, which is larger than the. Because of this, the mechanical advantage of single non-moving pulley is less than one. But this is advantageous, as a machine because the direction of applying could be changed appropriately. Mechanical advantage could be increased by using systems of pulleys. (see Fig : 3.17) 1 One moving and one non-moving pulley 3 4 One moving and two non-moving pulleys Two moving and two non - moving pulleys Two moving and three non-moving pulleys Fig : 3.17 Systems of pulleys Fig : 3.18 Crane as an application of system of pulleys The first system of pulleys shown in Fig: 3.17 consists of one moving pulley and one non-moving pulley. Here should be applied for a distance of two units to lift the by a distance of one unit. Therefore the velocity ratio is two. In the second system of pulleys in the figure, should be applied for a distance of three units to lift the by a distance of one unit. Therefore the velocity ratio of that system is three. Try to find the velocity ratios of the systems 3 and 4. For free distribution 57

14 Physics r Wheel and axle This is a type of machine which gives a rotating effect. Here the is applied to a wheel to r rotate it. That force is transmitted to an axle. 1 Think of the steering wheel of a motor vehicle. By applying a small to the wheel, the axle windlass ("dabaraya") could be rotated easily. This gives a large mechanical advantage. Velocity ratio circumference of wheel } circumference of axle } πr 1 πr } r 1 r Velocity ratio of wheel and axle } Radius of wheel Radius of axle Turning handle screw driver handle Engines Fig : 3.19 Wheel brace used to fix and remove wheel nuts Applications of wheel and axle blade The is applied to the handle. Then the blade rotates accordingly. Force is transmitted to rotate the through blade Task of engines is to rotate or to turn objects. This is done by transforming chemical energy stored in fuels into kinetic energy. Most of the ealier used engines were powered by steam. Fig : 3.0 A large steam engine used in workshops and mills Various types of engines ² Steam engine ² Turbine ² Internal combustion engine ² Jet engine ² Rocket engine Petrol, diesel, liquid petroleum gas (L.P.G) and electricity are used in engines today. 58 For free distribution

15 unit 3 Using mechanical energy for daily activities Comparison of some engines Petrol Diesel electric bio Type of engine Source of energy used Advantages Disadvantages Petrol Diesel Battery Food Efficiency is high Pollutes atmosphere Less expensive than petrol engines Heavier than others. Carbon deposits form easily. Pollutes atmosphere Less sound is emmited Air pollution is less Cannot store more energy Less sound Less air pollution Better for low speeds. Efficiency is low Do you know? Fig : 3.1 Steam engine invented by James Watt Fig : 3. Steam engine invented by Thomes Newcomon 300 years ago Summary ² Work is done when the point of application of a force moves. ² SI unit of measuring work is joule (J) ² Potential energy and kinetic energy are types of mechanical energy. ² Potential energy (gravitational) of an object is the energy stored due to its height of position. ² Energy stored in stretched rubber bands, wound springs etc. is elastic potential energy. ² Potential energy E p } mgh ² Kinetic energy E k } 1 $ mv For free distribution 59

16 Physics ² Law of conservation of energy states that energy could neither be created nor be destroyed. ² Power is the rate of work done. ² SI unit of power is watt (W) ² When work is done for 1 hour at a power of 1 kw, energy emitted is 1 kw h. ² Work could be eased by using simple machines and engines. ² Mechanical advantage of a simple machine ² Velocity ratio of a simple machine ² Efficiency of simple machine Load = Effort Distance moved by = Distance moved by (during the same time) = Mechanical advantage 100% Velocity ratio Exercises 1. i. How much is the amount of work done, when an object is lifted 4 m vertically up using a force of 10 N? ii. Calculate the work done when an object of 8 kg is lifted 0.5 m vertically up. iii. What is the type of energy stored in a stretched rubber band? iv. What is the type of energy stored in a fruit hanging in a tree? v. Find the amount of potential energy stored in an object of 1.5 kg, positioned at a height of 30 m. vi. Calculate the potential energy stored in an object of 750 g at a height of 80 m.. i. It took minutes for a machine to lift an object of 75 kg to a height of 80 m. What is the power of the machine? ii. If a work is done in a power of 60 W for 50 seconds, what is the amount of work done? iii. Calculate the kinetic energy of an object of 0 kg, moving at a velocity of 6 m s -1. iv. What do you mean by the law of conservation of energy? v. How do the machines ease work? 3. i. When an of 60 N is applied, a machine could suppress a of 180 N. What is its mechanical advantage? ii. When that is moved to a distance of 5 m, the machine moved the to a distance of 1 m. What is the velocity ratio of the machine? iii. What is the amount of work done on the machine (work input)? iv. What is the work output of the machine? v. Calculate the efficiency of the machine? 60 For free distribution

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