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WORK

Is defined as the product of the applied

force and the displacement of an object

in the direction of the applied force.

Work = Force x displacement

W = F X S

Unit = N m @ J (joule)

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F = 10 N

S = 2 m

F=5N

S

=1m

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Sometimes the object does not move in the direction of the applied force.To

calculate the work done by the force, the component of the applied force in the

direction of the displacement is used.

F

s

Since the object is displaced

horizontally, the horizontal

component of force is used.

Fx = F cos

Fy = F sin

F

S

Work = F cos x S

is the angel between Appliedforce F, and displacement , s !!!!

W = F cos

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example

F = 40 N

50

What is the work done in pulling the rock?

Solution:

Fx = F cos 50

Displacement = 6m

Work done = F Cos 50 x S

= 40 Cos 50 x 6m

= 154.26 J

S = 6m

S

Fy = Fsin 50

rock

W = F cos

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A person exerts a vertical force F = 20N on a pail as

the pail is carried a horizontal distance of 8.0 m at

constant speed.How much work does F do?

F

S

= 90 , F = 20N , S = 8m

Work , W = F Cos W = 20 Cos 90

= 0 J

No work is done by the vertical force because it has no

component in the direction of motion.

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Calculate work done by the force F

A

B

C

F = 10 N

F = 10 N

F = 10 N

S=2m

S=2m

S= 2m

W = F S

= 10 x 2 = 10J

( because is 0)

W = F x S

= 10 x 2 = 20 J

W = F Cos

= 10 Cos 180 (Cos 180 = -1)

= - 10 N

Now F and s are in opposite

direction.Therefore the work done is

negative.

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No Work is Done When:

The object is stationary

No force is applied on the object in the

direction of displacement

The direction of motion of the object is

perpendicular to the applie force

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QUIZCalculate work done by applied force, F following each situations.

F =200N

S = 6m

i

F=30N

S = 1.5m

pulley

ii

iii

A man pushing a wall .The

force applied is 200N but the

wall does not move.

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6

20

From the graph, Work = area under the graph

Eg: W = FS

= (20)(6)= 60 J

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ENERGY

The capacity

To do workUnit: J

Kinetic Energy

The energy of an object

due to its motion

Gravitional potential

Energy

The energy of an object

Due to its higher position

Ek = mv Ep = mgh

Energy Transfer When Work is Done

Change of Kinetic Energy = work done

Change of potential Energy= work done

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The relationship between Work and Energy

When work is done, energy

changes forms. For example,when you raise your physics

book vertically above your desk,

we say that "you do work on it".

This means, energy is being

converted from chemical

potential energy stored in yourmuscles to gravitational

potential energy of the book -

energy is changing forms. When

you let go of the book, gravity

"does work on the book". In

other words, gravitationalpotential energy is being

converted into kinetic energy -

work is changing forms. Work is

the process by which energy

changes forms.

The work Done = amount of

Energy

transfered

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1) What is the kinetic energy of man 50kg jogging at a velocity of 3 m/s?

Kinetic Energy, Ek = 1/2mv

= ( 50) (3)

= 225 J

2) A trolley with mass 4.0 kg pulled by force 20N along horizontal

frictionless track.

(a) What is the kinetic energy of a trolley after it pulled 10 m away?

(b) Calculate its vellocity after moved 10m.

(a) Ek = work done

= F x s= 20N x 10m

= 200J

1/2mv = 200

v = 400/4

= 100

= 10m/s

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Gravitional potential Energy

Example 1:A book of mass 2.0 kg rests ona table. If its gravitational potential

energy is 0 Joules now, what will its

gravitational potential energy be when it

is raised 1.0 meter above the table?

Solution: m = 2.0 kg, h = 1.0 m, g = 10m/s2

GPE = mgh = (2.0 kg)(10 m/s2)(1.0 m) =

20 Joules

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600

What is the work done by the force F,when the

box moved 5m?

Calculate the work done by the force of gravity on the

wooden block.(m= 0.2kg)

30

A man 65 kg walks from X to Y.Calculate the work

done.

W =30 Cos 60 x 5 = 75J

W = Energy tranfered

W = GPE = mgh

E = 0.2 x 9.8 x 2.5 = 4.9J

W = mgh

= 65 x 9.8 x 4 sin 30

= 1274J

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PRINCIPLE OF CONSERVATION of ENERGY

The Principle of conservation of energy

states that the total energy in a system

is

constant .

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A ball flew vertically upwards with initial velocity of 15

m/s . i) State the changes of energy

ii)What is the maximum height attained by the

ball?

i) Kinetic Enery to Gravitional potential energy

ii) m v2 = mgh

m x (15)2

= m x 10 x hh = 225 / 2x 10

h = 11.25 m

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h = 2m

Mass.m =1kg

SituationType of energy Total energy

A Ep 20 N

B Ep + Ek 20 N

C Ek 20 N

D Ep + Ek 20 N

E Ep 20 N

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In one of the activities at the National Service camp, a participant of 55 kg is to

climb up 2.5 m wall from ground level and jump down. Based on the jump of

the participant, calculate :

The speed of the participant just before his legs touch the ground

Potent ial Energy = Kinet ic Energy ( Tel l the student )

mgh = mv

v = 2gh

= 2 x 10 x 2.5= 7.07 ms-1

2

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Figure shows a roller coaster cart and a track. The cart is 250kg and start motion from rest

at A.

i)Calculate the potential energy of the cart at A

ii) Calculate the speed of the cart at point B

iii) Calculate the speed of the cart at point C

25000J

10m/s

14.14m/s

10m

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POWER

Poweris defined as the rateat which work is done or the

amount of work done persecond.

Power = Work done

Time taken

P = W

tThe SI unit of power is Watt (W) orJs-1When work is done, the object gains energy, therefore

Power = Change in energy

Time takenP = Et

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P = W

t

= F x st

= F x s

t

P = F x v where v- velocity

POWER

P = W

t

P = Et

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A motor lifts a barrel weighing 500N to a

vertical height of 1.5m in 25s. How much

power is used by the motor?

Power = work done

time taken

P = mgh

t

= 50 x 10 x1.5

25 = 30 W

10m/s

7N

2)

Wooden block

A wooden block being pulled with constant velocity 10m.

The force applied is 7N, to the horizontal along a table

surface. i) What is power output after 5s ?

ii)Calculate work done.

F = 7N, v= 10m/s, t=5s

Power, P = Fv ii) W =Pt

= 7 x 10 W = 70 x 5

= 70w W = 350J

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EFFICIENCY

Efficiency, = Energy output x 100%Energy input

Efficiency, = power output x 100%Power input

Example: A motor has a power1200w raised a mass of 50kg through a verticalheight of 20m in 10s.Its efficiency is:

Efficiency= power output x 100% Power output= W = mgh= 50(10)(20)

power input t t t

Efficiency = 1000 x 100% = 83.3%

1200

Check o r nderstanding

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1.A crane lift a load weighing 2400N

through a height of 4m in 12 s. What is the

power of the crane?

2. An alectric kettle is rated at 2kW

output is used to boil water. How many

joules of energy are transferred in 5

minutes?

3.A lift in a shopping complex can raise

10 people through a height of 25m in 15s.

The total mass is 1200kg. What is thepoweroutput of the lift motor?

4. A car of mass 800 kg travelling at 20m/s

slows to 10m/s. What is the change in

kinetic energy?

5. A car mass 600kg is travelling at 12m/s. When

the brakes are applied, it comes to rest in 8m.

What is the average force exerted by the

brakes?

6. A box 2 kg slides down a smooth curved

ramp. What is the speed of the box when it

reaches at the bottom

7. A motor pumps 40kg of waterfrom

ground level to a height of 6m in 2

minutes.What is the power output of

the motor

8. A motor with power 10kW raised a load

2.0 x 10 kg vertically. What is themaximum velocity of the load.

Check your understanding

Answer:

1.800W, 2.600kJ, 3. 20kW 4. 120kJ

5. 5400N 6. 8.9 m/s 7. 20W

8. 0.05 m/s

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