Physical Science Classes VI-X for School Assistants and TET Paper 2A · Chapter 3

Work, Energy, Power and Sound

What to remember

Work = force x displacement in the direction of the force (W = F s cos θ); SI unit joule. Energy is the capacity to do work, and power is the rate of doing work (watt = joule per second).
Mechanical energy has two forms: kinetic (½mv²) and potential (mgh). In a freely falling body the sum stays constant; energy is only changed from one form to another.
Sound is a longitudinal mechanical wave that needs a medium. Speed v = frequency x wavelength; pitch depends on frequency, loudness on amplitude, quality (timbre) on waveform.

Work

In science, work is done only when a force makes a body move. If a force F acts on a body and the body moves a distance s along the line of the force, then W = F x s. If the force makes an angle θ with the displacement, W = F s cos θ.

Unit: 1 joule (J) = 1 newton x 1 metre (N m).
Work is a scalar. It can be positive (θ less than 90°), negative (θ more than 90°, e.g. friction, or gravity on a rising body) or zero.
Work is zero when there is no displacement (pushing a wall), when the force is perpendicular to the displacement (carrying a bag while walking on level ground; the gravity force and the centripetal force in uniform circular motion), or when the force is zero.
Gravity does positive work on a falling body and negative work on a rising body.

Energy

Energy is the capacity to do work. Its SI unit is also the joule. Other units: 1 calorie = about 4.18 J; 1 kilowatt-hour (kWh) = 3.6 x 10⁶ J.

Kinetic energy (KE) is the energy due to motion: KE = ½ m v². It depends on mass and on the square of speed. If speed doubles, KE becomes four times. KE is never negative and has no direction.

Potential energy (PE) is the energy due to position or condition. Gravitational PE near the Earth = m g h. A stretched bow, a compressed spring and a wound watch spring store elastic PE. Water stored in a dam has gravitational PE.

Work-energy theorem: the work done by the net force on a body equals the change in its kinetic energy.

Law of conservation of energy: energy can neither be created nor destroyed; it changes from one form to another. For a freely falling body (air resistance ignored), at every point KE + PE = constant. At the top the energy is all PE; just before hitting the ground it is all KE, so v² = 2 g h.

Device	Energy change
Electric bulb	Electrical to light and heat
Electric motor	Electrical to mechanical
Generator (dynamo)	Mechanical to electrical
Microphone	Sound to electrical
Loudspeaker	Electrical to sound
Solar cell	Light to electrical
Battery (cell)	Chemical to electrical
Photosynthesis	Light to chemical

Sources of energy are called renewable (solar, wind, hydro, biomass) or non-renewable (coal, petroleum, natural gas).

Power

Power is the rate of doing work or the rate of using energy: P = W / t. SI unit: watt (W) = 1 joule per second. Larger units: 1 kilowatt = 1000 W; 1 megawatt = 10⁶ W. One horse power (hp) = 746 W.

Energy used = power x time. The commercial unit of electrical energy is the kilowatt-hour (kWh), called one "unit" on the electricity bill: 1 kWh = 1 kW x 1 hour = 3.6 x 10⁶ J.

Worked example: a 2 kW heater works for 5 hours. Energy = 2 x 5 = 10 kWh.

Worked example: a pump lifts 100 kg of water through 10 m in 20 s (g = 10 m/s²). Work = 100 x 10 x 10 = 10,000 J; power = 10,000 / 20 = 500 W.

Sound: production and propagation

Sound is produced by vibrating bodies (a tuning fork, a stretched string, an air column, the vocal cords). It travels as a wave through a material medium (solid, liquid or gas). It cannot travel through a vacuum; this is why astronauts on the Moon talk by radio.

In air, sound is a longitudinal wave: particles vibrate parallel to the direction of travel, forming alternate compressions (high pressure) and rarefactions (low pressure). Light and other electromagnetic waves, in contrast, are transverse and need no medium.

Wave terms:

Wavelength (λ): distance between two consecutive compressions or two consecutive rarefactions. Unit metre.
Frequency (f): number of vibrations per second. Unit hertz (Hz).
Time period (T) = 1/f.
Amplitude: maximum displacement of the particles from the mean position.
Wave speed: v = f λ.

Worked example: f = 500 Hz and λ = 0.68 m give v = 500 x 0.68 = 340 m/s.

Speed of sound. It is greatest in solids, less in liquids and least in gases: steel > water > air. In air at about 20 °C it is about 340 m/s (about 331 m/s at 0 °C), and it increases as temperature rises. It does not depend on the frequency or loudness of the sound. Sound travels slightly faster in moist air than in dry air.

Characteristics of sound

Characteristic	Depends on	Remark
Pitch	Frequency	High frequency gives a shrill sound
Loudness	Amplitude (and intensity)	Measured in decibel (dB)
Quality (timbre)	Waveform / overtones	Lets us tell two instruments apart on the same note

Women and children generally have higher-pitched voices than men because their vocal cords are shorter and thinner.

Audible range: 20 Hz to 20,000 Hz (20 kHz) for human beings. Below 20 Hz is infrasound (produced by earthquakes; used by elephants and whales to communicate). Above 20 kHz is ultrasound (heard by dogs and bats).

Uses of ultrasound: ultrasonography (scanning) in medicine, cleaning of delicate parts, detecting cracks in metal blocks, SONAR, and navigation of bats and dolphins.

Echo, reverberation and SONAR

Echo is the repetition of sound by reflection from a hard surface. The ear keeps a sound for about 0.1 second (persistence of hearing), so to hear a separate echo the reflected sound must come back after at least 0.1 s. With speed about 344 m/s at 20 °C, the reflecting surface must be at least about 17 m away.

Distance to a reflector: d = v t / 2 (the sound goes and returns). Example: an echo is heard after 2 s; with v = 340 m/s, d = 340 x 2 / 2 = 340 m.

Reverberation is the persistence of sound in a big hall because of repeated reflections. Too much of it makes speech unclear. Halls reduce it by using curtains, carpets, soft seats and perforated or rough walls. Sound boards (curved reflectors) are placed behind a stage to send sound to the audience.

SONAR (Sound Navigation And Ranging) sends ultrasonic pulses under water and times the echo to find the depth of the sea or the position of a submarine or a shoal of fish. Distance = (speed in water x time) / 2.

Human ear: outer ear (pinna and ear canal), eardrum, middle ear with three small bones (hammer, anvil, stirrup), inner ear with the cochlea that sends signals through the auditory nerve to the brain. The Eustachian tube equalises pressure.

Classroom angle

To show that sound comes from vibration, touch a vibrating tuning fork to a small ball hanging by a thread, or to water; the ball jumps and the water splashes.
A bell inside a jar from which air is pumped out is heard less and less. This shows that sound needs a medium.
A slinky spring shows compressions and rarefactions of a longitudinal wave.

Exam traps

Work done by a force perpendicular to motion is zero, not maximum.
Carrying a load horizontally: the person does no work against gravity in the physics sense.
Kilowatt-hour is a unit of energy, not of power.
Watt is a unit of power; watt-hour or joule is a unit of energy.
Doubling the speed makes KE four times, not two times.
Pitch is about frequency; loudness is about amplitude. They are not the same thing.
Sound is longitudinal; light is transverse.
Speed of sound is highest in solids; but speed of light is highest in vacuum.
The echo distance uses half of the total path: d = vt/2.

One-liners

1. SI unit of work and energy is the joule.
2. 1 J = 1 N m.
3. KE = ½ m v².
4. Gravitational PE = m g h.
5. Power = work / time; unit watt.
6. 1 hp = 746 W.
7. 1 kWh = 3.6 x 10⁶ J.
8. Audible range is 20 Hz to 20 kHz.
9. Loudness is measured in decibels.
10. Minimum distance for an echo is about 17 m.
11. SONAR means Sound Navigation And Ranging.
12. Sound cannot pass through a vacuum.

Practice questions

The SI unit of work is
1. watt
2. pascal
3. newton
4. joule
Answer
D. joule
Work = force x distance, measured in newton metre, which is the joule.
A force acts at right angles to the displacement of a body. The work done by the force is
1. equal to F x s
2. maximum
3. zero
4. negative
Answer
C. zero
W = F s cos 90 degrees = 0.
One horse power is equal to
1. 3.6 x 10^6 W
2. 376 W
3. 1000 W
4. 746 W
Answer
D. 746 W
1 hp = 746 watt.
If the speed of a moving body is doubled, its kinetic energy becomes
1. unchanged
2. two times
3. four times
4. half
Answer
C. four times
KE = 1/2 m v^2 depends on v squared, so doubling v gives 4 KE.
Sound cannot travel through
1. a vacuum
2. air
3. steel
4. water
Answer
A. a vacuum
Sound is a mechanical wave and needs a material medium.
In air, sound waves are
1. longitudinal
2. transverse
3. electromagnetic
4. stationary only
Answer
A. longitudinal
Air particles vibrate along the direction of travel of the wave.
The range of frequencies audible to a normal human ear is
1. 20 kHz to 200 kHz
2. 20 Hz to 20 kHz
3. 2 Hz to 2 kHz
4. 200 Hz to 200 kHz
Answer
B. 20 Hz to 20 kHz
Standard audible range is 20 Hz to 20,000 Hz.
Loudness of sound is measured in
1. watt
2. hertz
3. decibel
4. metre per second
Answer
C. decibel
The decibel (dB) is the unit of sound level.
The pitch of a sound depends on its
1. amplitude
2. speed
3. frequency
4. waveform only
Answer
C. frequency
Higher frequency gives a higher pitch.
The minimum distance of a reflecting wall needed to hear a distinct echo in air is about
1. 34 m
2. 17 m
3. 1.7 m
4. 170 m
Answer
B. 17 m
Persistence of hearing 0.1 s; d = 344 x 0.1 / 2 = about 17 m.
The speed of sound is greatest in
1. air
2. water
3. hydrogen gas at the same temperature as air
4. steel
Answer
D. steel
Sound travels fastest in solids, then liquids, then gases.
The commercial unit of electrical energy is
1. kilowatt-hour
2. joule
3. volt
4. kilowatt
Answer
A. kilowatt-hour
1 kWh is the unit charged on electricity bills.
The value of 1 kilowatt-hour in joule is
1. 746 J
2. 3.6 x 10^6 J
3. 3.6 x 10^3 J
4. 1 x 10^6 J
Answer
B. 3.6 x 10^6 J
1000 W x 3600 s = 3.6 x 10^6 J.
SONAR is used to
1. find the speed of light
2. measure air temperature
3. measure blood pressure
4. find the depth of the sea
Answer
D. find the depth of the sea
SONAR sends ultrasound under water and times the echo.
Loudness of a sound mainly depends on its
1. wavelength
2. amplitude
3. medium only
4. time period only
Answer
B. amplitude
Larger amplitude of vibration produces a louder sound.
A compressed spring has
1. elastic potential energy
2. kinetic energy only
3. no energy
4. heat energy only
Answer
A. elastic potential energy
Energy is stored due to its changed shape.
Power is defined as
1. energy x time
2. force per unit area
3. work done per unit time
4. force x distance
Answer
C. work done per unit time
P = W / t; unit watt.
A force of 10 N moves a body 5 m along the force. The work done is
1. 0.5 J
2. 2 J
3. 15 J
4. 50 J
Answer
D. 50 J
W = F s = 10 x 5 = 50 J.
A force of 20 N acts at 60 degrees to the displacement of 4 m (cos 60 = 0.5). The work done is
1. 20 J
2. 40 J
3. 160 J
4. 80 J
Answer
B. 40 J
W = 20 x 4 x 0.5 = 40 J.
The kinetic energy of a 2 kg body moving at 3 m/s is
1. 9 J
2. 18 J
3. 6 J
4. 12 J
Answer
A. 9 J
KE = 1/2 x 2 x 9 = 9 J.
A 5 kg body is raised through 10 m (g = 10 m/s^2). Its gain in potential energy is
1. 5000 J
2. 250 J
3. 500 J
4. 50 J
Answer
C. 500 J
PE = m g h = 5 x 10 x 10 = 500 J.
A motor does 3000 J of work in 10 s. Its power is
1. 30 W
2. 30000 W
3. 3000 W
4. 300 W
Answer
D. 300 W
P = 3000/10 = 300 W.
A 2 kW heater is used for 5 hours. The energy consumed is
1. 2.5 kWh
2. 10 kWh
3. 0.4 kWh
4. 7 kWh
Answer
B. 10 kWh
Energy = power x time = 2 x 5 = 10 kWh.
A sound has frequency 500 Hz and wavelength 0.68 m. Its speed is
1. 735 m/s
2. 170 m/s
3. 340 m/s
4. 680 m/s
Answer
C. 340 m/s
v = f x wavelength = 500 x 0.68 = 340 m/s.
An echo is heard 2 s after a shout. If the speed of sound is 340 m/s, the reflecting surface is at
1. 680 m
2. 170 m
3. 1360 m
4. 340 m
Answer
D. 340 m
d = v t / 2 = 340 x 2 / 2 = 340 m.
A body falls freely from rest through 5 m (g = 10 m/s^2). Its speed on reaching the ground is
1. 10 m/s
2. 25 m/s
3. 5 m/s
4. 50 m/s
Answer
A. 10 m/s
v^2 = 2 g h = 100, so v = 10 m/s.
The mass of a body is doubled and its speed is halved. Its kinetic energy becomes
1. double
2. four times
3. unchanged
4. half
Answer
D. half
New KE = 1/2 (2m)(v/2)^2 = 1/4 m v^2, which is half of 1/2 m v^2.
A sound of frequency 1700 Hz travels at 340 m/s. Its wavelength is
1. 0.5 m
2. 0.2 m
3. 5 m
4. 2 m
Answer
B. 0.2 m
Wavelength = v / f = 340 / 1700 = 0.2 m.
A SONAR pulse returns from the sea bed after 4 s. If the speed of sound in sea water is 1500 m/s, the depth is
1. 1500 m
2. 6000 m
3. 3000 m
4. 375 m
Answer
C. 3000 m
d = v t / 2 = 1500 x 4 / 2 = 3000 m.
A porter carries a load along level ground at constant speed. The work done by gravity on the load is
1. zero
2. positive
3. negative
4. equal to mg x distance
Answer
A. zero
The weight is perpendicular to the horizontal displacement.
Thunder is heard about 3 s after the lightning flash. If sound travels at 340 m/s, the lightning is about
1. 113 m away
2. 340 m away
3. 1020 m away
4. 3400 m away
Answer
C. 1020 m away
Distance = 340 x 3 = 1020 m; light reaches almost instantly.
A 60 kg student climbs a 3 m staircase in 6 s (g = 10 m/s^2). The power developed is
1. 300 W
2. 180 W
3. 1800 W
4. 30 W
Answer
A. 300 W
Work = 60 x 10 x 3 = 1800 J; P = 1800/6 = 300 W.
A teacher touches a vibrating tuning fork to a hanging ball and the ball jumps. This activity shows that
1. sound needs no medium
2. sound is produced by vibration
3. sound has no energy
4. sound is a transverse wave
Answer
B. sound is produced by vibration
Visible movement of the ball shows the fork is vibrating.
Astronauts on the Moon talk to each other using radio because
1. radio is cheaper
2. the Moon is too cold
3. sound is too weak on the Moon
4. there is no air to carry sound
Answer
D. there is no air to carry sound
Sound needs a medium; the Moon has no atmosphere.
An energy change of mechanical energy to electrical energy takes place in a
1. generator
2. microphone
3. electric heater
4. loudspeaker
Answer
A. generator
A generator converts mechanical work into electrical energy.
Which of the statements is/are correct? 1. Work is a scalar quantity. 2. Work done by a force can be negative.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
Work is a scalar and friction does negative work.
Which of the statements is/are correct? 1. Sound travels faster in water than in air. 2. Sound is a transverse wave in air.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Sound is faster in liquids than gases, but in air it is longitudinal.
Which of the statements is/are correct? 1. Kinetic energy depends on the direction of motion. 2. Power is the rate of doing work.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
KE is a scalar with no direction; power is work per unit time.
Which of the statements is/are correct? 1. Ultrasound has frequency above 20 kHz. 2. Elephants use infrasound to communicate.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
Both are standard facts.
Which of the statements is/are correct? 1. The speed of sound in air increases with temperature. 2. The speed of sound in air depends on its frequency.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Speed depends on the medium and temperature, not on frequency.
Which of the statements is/are correct? 1. Energy can be created from nothing in a machine. 2. For a freely falling body, KE + PE remains constant if air resistance is ignored.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
Energy is conserved; it is never created from nothing.
Which pair is correctly matched?
1. Pitch - amplitude
2. Loudness - frequency
3. Echo - refraction
4. Quality - waveform
Answer
D. Quality - waveform
Pitch relates to frequency, loudness to amplitude, quality to waveform; echo is reflection.
Which of the statements is/are correct? 1. A distinct echo needs a reflecting surface at a suitable distance. 2. Excessive reverberation improves clarity of speech in a hall.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Too much reverberation makes speech unclear.
Which of the statements is/are correct? 1. No work is done when a body moves in a circle at uniform speed. 2. Kinetic energy can be negative.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Centripetal force is perpendicular to motion; KE = 1/2 m v^2 is never negative.
Which of the statements is/are correct? 1. Sound needs a medium to travel. 2. Light needs a medium to travel.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Light travels through vacuum; sound cannot.

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1.The blades of a windmill rotate because of which of the following?
2.The formula to find the power is-
3.The elastic potential energy of a strained body is:
4.The energy possessed by a body due to its position or configuration is called ________.
5.The energy possessed by a ball of mass 5 kg when it is raised to a height of 5 m above the ground is (take g = 10 m/s 2):
6.The energy possessed by an object by virtue of its motion is known as ________.
7.The energy possessed by a moving object due to its motion is called:
8.The energy that is derived from the use of radioactive isotopes is termed as _________.
9.The SI unit of power is______.
10.The sum of _______ is mechanical energy.

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