WORK, ENERGY AND POWER

Work

The Concept of Work

Explain the concept of work

If  a  person  pushes  a  wall  and  the  wall  does  not  move,  though  the  person  may  sweat  and

physically  become tired, he would not  have done any  work. But if  the person pushes  a trolley

and the trolley moves it is said work is done.

The S.I Unit of Work

State the S.I unit of work

Work is the product of force and distance moved in the direction of the force.

Thus,

Work = Force (f) * distance (d) moved in the direction of the force.

SI unit of work is Joules.

The Work Done by an Applied Force

Determine the work done by an applied force

Example 1

A sack  of  maize,  which  weighs  800N, is  lifted to a height  of 2m.  What is  work done against

gravity?

Data given:

Force (f) = 800N

Height distance = 2m

Work done = ?

Solution:

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Work done (w.d) = force (f) x distance (d)

w.d = 800N x 2m

= 1600 Joules

Work done (w.d) = 1600Joules

Energy

The Concept of Energy

Explain the concept of energy

Energy can be defined as capacity of doing work.

Energy has the same SI unit like that of work, and that is Joules (J)

S.I Unit of Energy

State S.I unit of energy

Energy has the same SI unit like that of work, and that is Joules (J)

Different Forms of Energy

Identify different forms of energy

There are different forms of ener gy such as:

1.

Chemical energy

2.

Heat energy

3.

Light energy

4.

Sound energy

5.

Electrical energy

6.

Nuclear energy

7.

Solar energy

Difference between Potential Energy and Kinetic Energy

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Distinguish between potential energy and kinetic energy

There are two types of chemical energy, which are:

1.

Potential energy:It is the energy possessed by a body mass in its position or state.

2.

Kinetic energy: It is the energy possessed by a body due to its motion.

Consider  when  the  body  is  vertically  thrown  upwards  with  an  initial  velocity  „u   f rom  the

ground.

At the ground:

The height is zero and initial velocity is at maximum so as to attain maximum

height.

Therefore K.E = ½ MV

will be maximum

2

K.E

= ½ mv

2

max

Where K.E = Kinetic energy

M = Mass of the object/body

V=Velvety

P.E = Mgh

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Where

P.E = Potential energy

M= Mass of the object

H = Height of the object

g = gravitation force

P.E = Mgh will be zero because P.E

= M*g*0 (body at the ground where k=0)

Neglecting  the  air  resistance,  as  the  body  moves  upwards  its  velocity  decreases  it  also

experiences gravitational force (g) pulling downwards towards the earth s centre.

The maximum Height Attained

The final velocity of the body will be zero (V=0)

Therefore K.E = ½ mv

2

K.E = ½ m(0)

2

K.E = 0

P.E = MgHmax

Note:

That the object drops from Hmax that is; it leaves with zero Kinetic Energy. At position A

in fig. 8. The conservation of mechanical energy (M.E) is given as:

P.E + K.E = Constant

(The sum of P.E and K.E is constant throughout the motion of the object if the air resistance is

neglected)

The Transformation of Energy

Explain the transformation of energy

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The  notion  of  energy  is  that  energy  is  changed  from  one  form  into  different  forms  using

transducers.

Transducer is a device used to transform energy from one form to another.

For example:

1.

Battery converts chemical energy into electrical energy.

2.

A generator converts mechanical energy into electrical energy.

3.

A motor converts electrical ener gy into mechanical energy.

The Table Summarising Energy Transformation

ORIGINAL ENERGY  TRANSDUCER  ENERGY TRANSFORMED

Chemical energy  Battery  Electrical energy

Chemical energy  Motor  Chemical energy

Mechanical energy  Generator  Electrical energy

Solar energy  Solar panel  Electrical energy

Chemical energy  Motor car  Mechanical energy

Electrical energy  Microphone  Sound energy

Electrical energy  Heater  Heat energy

Activity 1

To demonstrate pressure of potential ener gy.

Materials and Apparatus

1.

A heavy stone

2.

A bucket full of water

3.

A strong inelastic rope; and

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4.

Smooth pulley

Procedures:

Collect the heavy stone, using a strong rope tie it to a bucket of water

Pass the rope over smooth pulley fixed to a support.

Hold stationary the heavy stone at height “h” above the ground

Release the stone

Results and observations:

When the stone released the bucket of water will start to rise.

The stone is said to have potentials energy because of its position above the ground.

Lifting a body of mass “m” to a height “h” above the ground requires work to  be done

against gravity. Work = Mgh

Example 2

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A ball of mass 0.5 kg is kicked vertically upwards and rises to a height of 5m. Find the potential

energy by the ball.

Data given:

Mass of the ball (Mb) = 0.5 kg

Height (h) = 5m

Gravitation force (g) 10N/kg

Potential energy (P.E) = ?

Solution:

Potential energy (P.E)= mgh

= 0.5kg x 10N/kg x 5m

= 25 NM

1NM= 1Joules

Potential energy (P.E) = 25 Joules.

Activity 2

Aim: to investigate the law of conservation of energy by a simple pendulum.

Materials and Apparatus:

A pendulum bob and light inelastic string.

Producers

Pull the bob of a simple pendulum in position A so that it is at height “h” above position

B.

Release the bob so that it swings to position C via the lowest position B and back to A.

Consider the figure below:

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Observation

When the bob is at position A, it possesses potential ener gy only due to the height “h” which is

equal to “Mgh”.

As it swings downwards to position B, the height decreases, and  as the result it loses potential

energy.

The bob has Vmax and hence K.Emax at B. The height at B is zero, thus the P.E is zero.

As it swings towards C, the P.E increases and reaches its maximum again in position C,

where  the Kinetic  Energy  is  zero.  At  position D, the  energy  of the bob is  party  potential  and

party Kinetic.

The Principle of Conservation of Energy

State the principle of conservation of Energy

The law of conservation of energy state that “ Energy can neither be  created nor destroyed but

can only be converted from one form to another.”

This means the amount of energy is constant all the time.

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Example 3

A stone of  mass 2kg is released form a height of 2m above the ground. Find the potential energy

of the stone when it is at the height of 0.5m above the ground.

Data given;

Mass of the stone (Ms) = 2kg

Height released (h) = 2m

Gravity (g) = 10N/kg

Potential energy = (P.E) ?

Solution:

P.E at height g 2m

P.E = Mgh

= 21g x 10N/kg x 2m

P.E = 40 Joules

P.E at 2m = 40Joules

Than P.E at height of 0.5m

= 21g x 10N/kg x 0.5m

P.E at 0.5m = 10Joules

100s of P.E = 40 Joules - 10Joules

= 30 Joules

According to conservation of energy the loss of P.E should be equal to the gain in K.E, when the

air resistance is neglected.

K.E of the stone at 0.5 above the ground = 30 Joules

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Example 4

A ball of mass 0.21kg is dropped from a height of 20m. on impact with the ground it loses 30J of

energy. Calculate the height which it reaches on the rebound.

Data given;

Mass of ball (Mb) = 0.2kg

Height dropped (h) = 20m

Loose in energy (E) 30J

Height which reaches=?

Solution;

Consider the figure below;

At 20m above ground the initial energy of the ball = Mgh

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= 0.2kg x 10N/kg x 20m

= 40 Joules.

So after the impact the ball loose 30J and the energy remaining is 40 J-10J

= 10Joules

At the top of rebound the energy of the ball = potential energy (P.E)

The height reaches (h) is 5m.

Uses of Mechanical Energy

Explain the uses of mechanical energy

The mechanical energy can be  used to produce electric  power using generators.  Some  uses  of

mechanical energy are: It enables our body to do work, it makes work easier and faster, it is used

to  transport  goods  and  people  from  one  place  to  another,  many  transport  vehicles  uses  the

knowledge  of  mechanical  energy.  Examples  of  vehicles  which  uses  mechanical  energy  are

airplanes and motor cars.

Power

The Concept of Power

Explain the concept of power

Power is the rate of which work is done.

It is a measure of the rate at which energy changes.

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This means that whenever work is done energy changes into a different form.

The S.I Unit of Power

State the S.I unit of power

The SI unit of power is Jules per second J/S or watts, W.

1 Joules per second = 1 watt

When 1 Joules of work is  done per second  the  power produced is  a watt. Watt is  the  unit  for

measuring electrical power.

The Rate of Doing Work

Determine the rate of doing work

Suppose that two cranes each lift objects having masses of 200kg to a height of 12m. Crane A

lifts its object in 10sec while crane B requires 15sec to lift its object. Assume they lift the objects

at a constant velocity they do the same amount of work.

Work done = GPE

= Mgh

= (200kg) (9.8m/s

(12m)

2)

= 23520J

Each did a work that was equivalent to 23520J.

What is different for the two cranes is the rate at which they did the work or their generation of

power.

The power of crane A can be calculated by;

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P

= 1568 watts.

B

Example 5

How much power is required to accelerate a 1000kg car from rest to 26.7m/s in 8sec?

Solution:

The work done on the car increases its Kinetic energy.

Work done = AKE

½ MV

2

– ½ MV

2

The power required is given by:

Example 6

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Car  engine  is  rated  in  horsepower  (hp)  where  1hp  =  746watts.  What  is  the  required  power

measured in horsepower?

Since work causes a change  in  ener gy.  DE  power can be considered  as  the  rate of  change  of

energy.

P = DE/t

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