As h 21d Workenergy&Power

8/12/2019 As h 21d Workenergy&Power

1/31

Work (W)

Work is done when a force moves its point ofapplication.

work = force x distance moved in thedirection of the force

W = F s

unit: joule (J)work is a scalarquantity


2/31


3/31


4/31

Question 2

Calculate the work done by a child of weight 300N who

climbs up a set of stairs consisting of 12 steps each of

height 20cm.

wo rk = force x distance

the child must exert an upward force equal to its weight

the distance moved upwards equals (12 x 20cm) = 2.4m

work = 300 N x 2.4 m

work = 720 J


5/31

Question 3

Calculate the work done by

the wind on the yacht in the

situation shown below:

wind force = 800 N

distance moved

by yacht = 50 m

30


6/31

Complete:

Force Distance Angle betweenFand s

Work

400 N 5 km 0 2 MJ

200 N 300 m 0 60 mJ

50 N 6 m 60 150 J

400 N 3 m 90 0 J


7/31

Force-distance graphs

The area under thecurve is equal to

the work done.

F

s

force

distance

area = work done

F

s

force

distance

area = work

= F s

area = work

found by

countingsquares on

the graph

F

s

force

distance


8/31

Question

Calculate the work done by

the brakes of a car if theforce exerted by the brakesvaries over the cars brakingdistance of 100 m as shownin the graph below.

2

force / kN

distance / m

1

50 100

area B

area A


9/31

Energy (E)

Energy is needed to move objects, to changetheir shape or to warm them up.

Work is a measurement of the energy required to

do a particular task.

work done = energy change

unit: joule (J)


10/31

Conservation of Energy

The principle of the conservation ofenergy states that energy cannot be

created or destroyed.

Energy can change from one form to

another.

All forms of energy are scalar quantities


11/31

Some examples of forms of energyKinetic energy (KE)

Energy due to a bodys motion.Potential energy (PE)

Energy due to a bodys position

Thermal energy

Energy due to a bodystemperature.

Chemical energy

Energy associated with chemical

reactions.

Nuclear energy

Energy associated with nuclearreactions.

Electrical energy

Energy associated with electric

charges.

Elastic energy

Energy stored in an object when it

is stretched or compressed.

All of the above forms of energy (and others) can

ultimately be considered to be variations of kinetic or

potential energy.


12/31

Kinetic Energy (EK)

Kinetic energy is the energy an object hasbecause of its motion and mass.

kin etic energy = x mass x (speed)2

EK= m v2

Note: v= speed NOTvelocity.

The direction of motion has no relevance to kineticenergy.


13/31

Question 1

Calculate the kinetic energy of a car of mass800 kg moving at 6 ms-1

EK= m v2

= x 800kg x (6ms-1)2

= x 800 x 36

= 400 x 36

kinetic energy = 14 400 J


14/31

Question 2

Calculate the speed of a car of mass 1200kg if itskinetic energy is 15 000J

EK= m v2

15 000J = x 1200kg x v2

15 000 = 600 x v2

15 000 600 = v2

25 = v2

v= 25

speed = 5.0 ms-1


15/31

Question 3

Calculate the braking distance a car of mass 900

kg travelling at an initial speed of 20 ms-1if itsbrakes exert a constant force of 3 kN.


16/31

Complete:

Mass Speed K inetic energy

400 g 4.0 ms-1 3.2 J

3000 kg 10 kms-1 60 mJ

8 kg 300 cms-1 36 J

50 mg 12 ms-1 3.6 mJ


17/31

Gravitational Potential Energy (gpe)

Gravitational potential energy is theenergy an object has because of itsposition in a gravitational field.

change in g .p .e.

= mass x gravi tat ional f ield strength

x change in height

EP= m g h


18/31

Question

Calculate the change in g.p.e. when a massof 200 g is lifted upwards by 30 cm.

(g = 9.8 Nkg-1)

EP= m g h= 200 g x 9.8 Nkg-1x 30 cm

= 0.200 kg x 9.8 Nkg-1x 0.30 m

change in g.p.e. = 0.59 J


19/31

Complete:

mass gh

EP

3 kg 10 Nkg-1 400 cm 120 J

200 g 1.6 Nkg-1 30 m 9.6 J

7 kg 10 Nkg-1 4000 m 280 kJ

2000 g 24 Nkg-1 3000 mm 144 J


20/31

Falling objects

If there is no significant

air resistance then the

initial gravitational

energy of an object is

transferred into kineticenergy.

EK= EP

m v2 = m g h

h

m

h

v1

v2

gpe = mgh

ke = mv22

ke = 0

gpe = 0

gpe = ke

gpe = mgh

ke = mv12

ke = mgh


21/31

QuestionA child of mass 40 kg climbs up a wall of height 2.0 m

and then steps off. Assuming no significant air resistancecalculate the maximum:

(a) gpe of the child

(b) speed of the child

g= 9.8 Nkg-1


22/31

Power (P)

Power is the rate of transfer of energy.

power = energy transfer

t imeP = E

t

unit: watt (W)

power is a scalar quantity


23/31

Power is also the rate of doing work.

power = work done

t ime

P = W

t


24/31

Question 1

Calculate the power of an electric motor that lifts a mass

of 50 kg upwards by 3.0 m in 20 seconds.

g= 9.8 Nkg-1


25/31

Question 2

Calculate the power of a car engine that

exerts a force of 40 kN over a distance of 20

m for 10 seconds.


26/31

Complete:

energytransfer wo rk done t ime power

600 J 600 J 2 mins 5 W

440 J 440 J

20 s 22 W

28 800 J 28 800 J 2 hours 4 W

2.5 mJ 2.5 mJ 50 s 50 W


27/31

Power and velocity

power = work done / t ime

but: work = force x disp lacement

therefore: power = force x disp lacement

t ime

but:disp lacement / t ime = veloci ty

therefore:

power = force x veloc i tyP = F v


28/31

Question

Calculate the power of a car that maintains a

constant speed of 30 ms-1against air resistance

forces of 2 kN


29/31

Energy efficiency

Energy efficiency is a measure of howusefully energy is used by a device.

efficiency =

useful energy transferred by the device

total energy supplied to the device

As the useful energy can never be greater

than the energy supplied the maximumefficiency possible is 1.0


30/31

Also:

efficiency =useful work output

energy supplied

useful power outputefficiency =

power input

In all cases:

percentage efficiency = efficiency x 100


31/31

Complete

Input

energy (J)

Useful

energy (J)

Wasted

energy (J)

Efficiency Percentage

efficiency

100 40

250 50

50 0.20

80 30%

60 60

Documents

As h 21d Workenergy&Power