Using mechanical energy for daily

Using mechanical energy for daily activities

Chapter 3 Physics

Competency

Uses mechanical energy for day-to-day activities

Competency level Subject content

3.1 Investigates how mechanical energy is used to do work

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

3.2 Estimates the value of mechanical energy

3.3 Investigates various methods to make work easy

² Potential energy, E_P= mgh

² Kinetic energy E_k = ½ mv²

² Calculations related to energy

² Nature of conservation of energy

² Simple machines and engines

² Mechanical advantage

² Velocity ratio

² Efficiency

Energy means the ability to do work. Energy is spent when work is done. There are various forms of energy such as,

Mechanical energy Electrical energy

Heat energy Sound energy

Chemical energy Light energy Magnetic energy

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 2 m = (5 x 2 ) = 10 J

1 J

work done

1 m

1 N

Fig : 3.1 An instance where work of one joule is done.

Work done = Force × Displacement of the point of action of force (towards the direction of force)

1 000 J = 1 kJ (kilo joule) 1 000 000 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

20 N 6 m ...

... 8 m 200 J

40 N 50 cm ...

30 N ... 24 J

120 N 0.4 m ...

3.1

How mechanical energy is used to do work

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

Knowledge check

1. Find the amount of work done, when an object of a mass of 12 kg is lifted to a height of 3 m

2. 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 25 kg is lifted to a certain height, the work done is 200 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^-2]

Here an amount of 400 J of energy is transmitted into the object.

Fig : 3.2 weight of a mass of 1 kg is 10 N.

Fig : 3.3 Force exerted to lift a mass of 1 kg.

weight

10 N

g = 10 m s^-2

1 kg

mass

1 kg 10 N

10 N

Mechanical energy

Mechanical energy is of two types.

1. Potential energy 2. 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 200 m high is 8 kg.

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.

Fig : 3.4 Energy stored in a stone positioned on a hill top is gravitational potential energy

Fig : 3.5 Energy stored in a stretched spring is elastic potential energy

Gravitational potential energy } m « g « h This value is obtained by 8 kg « 10 m s^-2 « 200 m

Mass (m)

acceleration due to gravity (g)

height(h)

Energy stored in an object due its position of height is known as gravitational potential energy.

Weight of the stone = 8 kg « 10 m s^-2 = 80 N Work done when it

falls 200 m down = 80 N « 200 m

= 16000 J Therefore the energy stored in

the piece of stone (potential energy)

= 16000 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 2. Flowing water 4. Flying bird

There is a coconut with a mass of 2.5 kg at the height of 20 m on a coconut tree.

Calculate the potential energy stored in the coconut. (g = 10 m s^-2)

Mass of the coconut = 2.5 kg

Height to the coconut = 20 m Potential energy stored in it = mgh

= 2.5 kg x 10 m s^-2 x 20 m

= 500 J

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 2. Speed of the object

v t

v t 0 + v 2

v

= 2

v 2

« t

1 2 mv² Kinetic energy is denoted by E_k

Assume an object of mass m, zero initial speed and speed v after time t.

Acceleration of a moving object, a =

Force acting on the moving object, F = ma

= m «

Mean (average) speed =

Distance Moved = mean velocity « time

=

Work done = Force « distance moved

Kinetic energy of the object

Kinetic energy stored in an object

of mass m, moving in velocity v

}

mv

t « v t

=

^ & ^

&

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 5 000 W. It can do an amount of work of 5 000 J per second.

Do you know ?

Calculations related to kinetic energy

Example 1

What is the kinetic energy contained in an object of the mass of 2 kg, moving in a velocity of 6 m s^-1 ?

Example 2

What is the kinetic energy stored in an object of 5 kg, moving in a velocity of 10 m s^-1 ?

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.

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.

Fig : 3.6 James Watt. Unit of measuring power is named after this scientist, who is also

the inventor of steam engine.

Power = Work done Time taken

Let amount of work done in 10 seconds is 600 J;

Power = 600 J = 10 s

J s⁻¹ is Watt (W). Unit of measuring power is Watt (W)

E_k = mv²

= « 2 kg ^« (6 m s⁻¹)² = « 2 kg ^« 36 m² s⁻²

= 36 J

1 2 1 2 1 2

E_k= mv²

= « 5 kg ^« (10 m s⁻¹)² = « 5 kg ^« 100 m² s⁻²

= 250 J

1 2 1 2 1 2

60 J s⁻¹

Kinetic energy,

Kinetic energy,

1 J = 1 kg m² s^-2

Think of a machine of 1 kW. The power of it is 1000 W. 1000 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)

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 20 h in that power, how much energy was spent ?

Amount of energy spent = Power « Time

= 1.5 kW x 20 h

= 30 kW h

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 load in one point is supressed by a force (effort) applied to another point.

Given below are some commonly used simple machines.

² Lever

² Inclined plane (ramp)

² Pulley

² Wheel and axle

1 kW = 1 000W = 1 000 J s^-1

∴ Energy spent in 1 s = 1 000 J

1 h = 3 600 s

Energy spent in 3 600 s = 1 000 J s^-1 × 3 600 s

= 3 600 000 J

∴ 1kW h = 3 600 000 J

Fig : 3.7 Lever

Methods of making Jobs easy

Fig : 3.8 Inclined plane

Mechanical Advantage =

Velocity ratio

Ratio of the velocity of motion of effort to that of load is the velocity ratio. But both effort and load moves in the same time.

Therefore velocity ratio could be obtained by dividing the distance of the movement of effort by that of load.

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, load should be multiplied by the distance moved by load.

Fig : 3.9 Pulley

Fig : 3.10 Wheel and axel

In every machine, effort is applied to one point and it is transmitted to the load acting on another point of the machine.

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 effort. The force suppressed by the machine by applying the effort is called load.

Mechanical advantage of a machine is the ratio of the load suppressed (L) to the effort applied (E)

How we can making work easy by machines ?

1' Work that needs a large effort could be done by applying smaller effort on the machine.

2' Direction of applying force could be changed.

3' Rate of doing work could be increased.

Load Effort

= L E

Distance moved by effort Distance moved by load.

Velocity ratio =

That amount of work is done by the machine because of the work done by the effort on the machine.

If the effort exerted on the machine, in the above instance is 200 N and the distance moved by the effort is 80 cm;

Work done on the machine or

work input = ^200 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 120 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.

In the above example;

Work input = 160 J Work output = 120 J

Then what will be the work output, if work input is 100 J ?

Work output = 600 N « 20 m = 120 J 100

This result is known as efficiency of the machine. It is always given as a percentage.

120

160 « 100]

It will be = 75]

Efficiency =

Efficiency = _{× 100%}

effort × distance moved by effort load × distance moved by load

= ^load

effort ÷ distance moved by effort

distance moved by load × 100%

= mechanical advantage ÷ velocity ratio × 100%

∴ Efficiency =

× 100%

Work Input Work output

× 100%

velocity ratio mechanical advantage

}

If load is 600 N and distance moved by load is 20 cm.

Effective work or the work output of a machine=Load × distance moved by load

Work done on the machine (work input) = Effort × Distance moved by effort

Always the work output of a machine in practice is less than the work input of it.

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.

Levers

A lever is a bar which can be moved freely round a pivot

First order levers

Here fulcrum is positioned in-between the load and effort.

Pair of scissors, pair of pliers, and see-saw are some examples for first order levers. (Fig : 3.12)

Effort Load

Fulcrum

See-Saw

Pair of pliers Pair or scissors

Fig : 3.12 First order levers Fig : 3.11 Lever as a simple machine

fulcrum

effort arm

effort load arm

load

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 load. Force applied on the lever is the effort. Distance from the point of action of load to the fulcrum is length of load arm. Distance from the point of action of effort to the fulcrum is the length of effort arm. If the effort arm is longer than the load arm of a lever, more load could be lifted by applying less effort.

There are three types (or orders) of levers according to the relative positions of effort, load and fulcrum.

Third order levers

When fulcrum is at one end, load is at the other end and the effort is applied in-between those two; such levers are called third order levers. Forcep, broom and fishing rod are some examples.

Inclined plane

Ramps or inclined planes are also used to ease work. You may have seen how barrels of oil are loaded 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 2' Screw nail 6' Stair case

3' Ladder 7' Cutting edge of a knife 4' Chisel 8' Winding roads in

mountains.

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.

Fulcrum

Load Effort

Fulcrum

Load

Nut cracker

Wheel barrow

Fig : 3.14 Third order levers

Effort

Fig : 3.13 Second order levers.

ramp to load weights Using

Fig : 3.15 Inclined plane

Wedge Screw nail

Fishing rod forcep

load effort 1500 N 500 N

^III& Velocity ratio } } } 4

^IV& Efficiency of the inclined plane }

} «100% } 75%

Distance moved by effort Distance moved by load

^I& Mass of object } 150 kg

∴ Its weight } 150 kg « 10 m s^-2 } 1500 N

^II& Mechanical advantage } } } 3

^I& What is the weight of the object (load) ? (g=10 m s^-2)

^II& What is the mechanical advantage of this inclined plane ?

^III& What is its velocity ratio ?

^IV& Calculate the efficiency of the inclined plane.

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 effort is applied to the other end. As the distance moved by the effort and the distance moved by load are equal, the

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 (effort) is 500 N.

3 4

Fig : 3.16 Pulley as a simple machine

4 m 1 m

effort

load

4 m 500 N

1 m 1500 N

Mechanical advantage «100%

Velocity ratio Solved Example

The first system of pulleys shown in Fig: 3.17 consists o f one moving pulley and one non-moving pulley. Here effort should be applied for a distance of two units to lift the load by a distance of one unit. Therefore the velocity ratio is two.

In the second system of pulleys in the figure, effort should be applied for a distance of three units to lift the load 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.

Fig : 3.18 Crane as an application of system of pulleys

velocity ratio of single pulley is one (Fig : 3.16) But load cannot be lifted up by applying an equal effort because of the friction of the pulley. Therefore it is necessary to apply an effort, which is larger than the load. 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 effort could be changed appropriately.

Mechanical advantage could be increased by using systems of pulleys. (see Fig : 3.17)

effort

load

effort effort

effort

load

load

load

Fig : 3.17 Systems of pulleys One moving and

one non-moving pulley

One moving and two non-moving

pulleys

Two moving and two non - moving

pulleys

Two moving and three non-moving

pulleys

1 2 3 4

load effort

Engines

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 en- gines were powered by steam.

Fig : 3.20 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.

Wheel and axle

This is a type of machine which gives a rotating effect. Here the effort is applied to a wheel to rotate it. That force is transmitted to an axle.

Think of the steering wheel of a motor vehicle.

By applying a small effort to the wheel, the axle could be rotated easily. This gives a large mechanical advantage.

r₂

r₁

circumference of wheel circumference of axle

Velocity ratio }

∴ Velocity ratio of wheel and axle }

screw driver

The effort is applied to the handle. Then the blade rotates accordingly. Force is transmitted to rotate the load through blade Turning

handle

Fig : 3.19 Applications of wheel and axle

handle

blade

effort

load

2πr₁

2πr₂ } r₁ r₂

Radius of wheel Radius of axle

Wheel brace used to fix and remove wheel nuts

windlass ("dabaraya")

}

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$

2 mv² Comparison of some engines

Type of engine

Petrol Diesel electric bio

Petrol Diesel Battery Food

Source of energy used

Efficiency is high

Less expensive than petrol engines

w Less sound is emmited w Air pollution is less

w Less sound w Less air pollution w Better for low speeds.

Advantages

Cannot store more

energy Efficiency is low

Disadvantages

Fig : 3.22 Steam engine invented by Thomes Newcomon 300 years ago

Fig : 3.21 Steam engine invented by James Watt

Do you know ?

Heavier than others.

Carbon deposits form easily.

Pollutes atmosphere

Pollutes atmosphere

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.

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.

2. i. It took 2 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 20 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 effort of 60 N is applied, a machine could suppress a load of 180 N. What is its mechanical advantage?

ii. When that effort is moved to a distance of 5 m, the machine moved the load 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?

² Mechanical advantage of a simple machine

= Load

Effort

² Velocity ratio of a simple machine

Distance moved by effort

= Distance moved by load (during the same time)

² Efficiency of simple machine Mechanical advantage

= Velocity ratio × 100%