Notes: Work, Power & Energy | Science & Pedagogy Paper 2 for CTET & TET Exams - CTET & State TET PDF Download

Applying forces to perform work, utilizing various forms of energy, and generating power are all interconnected. When work is done by applying a force to a body, it produces different forms of energy that can be transformed into any desired form, benefiting mankind. Energy can be converted into work through mechanical devices, and there is also the conversion of mass into energy and vice versa, famously described by Einstein's mass-energy relation.

Work

In physics, work is done when a force is applied to an object and it is displaced. Mathematically, work is expressed as the product of the applied force and the displacement of the body in the direction of the force:

Formula: W = F x d = F x cos θ x d  ,where  θ is the angle between the force and the displacement.

The SI unit of work is Joule (J).

Nature of Work in Various Situations:

1. Positive Work: If the force and the direction of displacement are the same, then work done is positive. Example: When a horse pulls a cart.
2. Negative Work: If the force is opposite to the direction of displacement, then work done is negative. Example: When brakes are applied to a moving vehicle.
3. Zero Work: Work done by a force is zero when the displacement is perpendicular to the applied force. Example: Tension in a string of a simple pendulum.

Power

The rate of doing work is called power. The power delivered by a force is given by:

Formula:  , where  v  is the velocity of the object.

The SI unit of power is Joule/second, known as Watt (W). A commonly used unit of power is horsepower:

1 horsepower (hp) = 746 watts.

Energy

Energy is the ability or capacity to do work. It exists in various forms:

1. Mechanical Energy: The energy of an object due to its motion or position.
2. 
   
   1. Kinetic Energy (KE): The energy possessed by an object due to its motion. Formula: , where m is the mass and v  is the velocity of the object.
   2. Potential Energy (PE): The energy possessed by an object due to its position. Formula: PE = mgh , where  m  is the mass,  g is the acceleration due to gravity, and  h  is the height or position of the object.
3. Heat Energy: The energy possessed by a body due to the random motion of its molecules. It is related to the internal energy of the body.
4. Light Energy, Sound Energy, Electrical Energy, Chemical Energy, Solar Energy, Nuclear Energy: Various other forms of energy.

Law of Conservation of Energy

This law states that energy can neither be created nor destroyed, but can only be transformed from one form to another. The total energy of any body or system remains constant.

Example: When a body falls from a height, its potential energy is converted into kinetic energy.

Scales of Temperature

Temperature is the degree or intensity of heat present in a substance or object, typically measured using a thermometer or perceived by touch. There are four main scales for measuring temperature:

1. Celsius Scale: Ice point is 0°C and steam point is 100°C.
2. Kelvin Scale: Ice point is 273 K and steam point is 373 K.
3. Fahrenheit Scale: Ice point is 32°F and steam point is 212°F.
4. Reaumur Scale: Lower fixed point is 0°R and upper fixed point is 80°R.

Relation between Different Scales:

Conversion formulas:

From	To	Formula
Celsius (C)	Fahrenheit (F)
Celsius (C)	Reaumer (R)
Celsius (C)	Kelvin (K)

Thermometer

A thermometer is a device used to measure temperature. The most common type is the mercury thermometer, widely used in medical and laboratory settings.

Different Kinds of Thermometers:

1. Clinical Thermometer: Used to measure body temperature, typically ranging from 35°C to 42°C.
2. Laboratory Thermometer: Used in laboratory settings, with a range of 10°C to 110°C.

Terms Related to Heat Energy

1. Heat Capacity: The amount of heat required to raise the temperature of a substance by 1°C.
2. Specific Heat Capacity: The amount of heat required to raise the temperature of a unit mass of a substance by 1°C.
3. Melting Point: The temperature at which a substance changes from solid to liquid state.
4. Boiling Point: The temperature at which a substance changes from liquid to gas state.

Modes of Transfer of Heat

Heat flows from a body at higher temperature to a body at lower temperature. There are three modes of transfer of heat:

1. Conduction: Transfer of energy between different parts of a body or from one body to another body in contact with each other.
   • Heat transfer in solids occurs through conduction.
   • Conductor: A substance through which heat flows easily, such as metals. Silver is the best conductor.
   • Insulator: A substance through which heat does not flow easily, such as paper, glass, wood, and plastic. Air is also a bad conductor of heat.
   • Woollen clothes keep us warm during winter because wool is a poor conductor of heat and traps air between its fibres.
2. Convection: Heat is transferred by the actual motion of heated material, typically in liquids or gases.
   • Examples include land and sea breezes, and the use of ventilators and exhaust fans.
   • Forced convection is the main mechanism of heat transfer inside the human body.
3. Radiation: Heat is transferred from one body to another without any contact or presence of a medium.
   • Thermal radiation is electromagnetic radiation that travels in straight lines at the speed of light.
   • Dark-colored objects absorb more heat than light-colored objects. Hence, we wear light-colored clothes in summer.
   • The heat from the sun reaches the Earth by radiation.

Other Important Terms Related to Heat Energy

• Latent Heat: The energy required by unit mass of a substance to change from one state to another without a change in temperature.
• Latent Heat of Fusion of Ice: 80 cal/g or 335 J/g.
• Latent Heat of Vaporisation of Water: 50 cal/g or 2260 J/g.

Light Energy

Light helps us see objects and travels in a straight line, known as rectilinear propagation of light.

• Luminous Objects: Objects that emit their own light.
• Non-Luminous Objects: Objects that do not emit their own light.
• A pinhole camera works on the principle of rectilinear propagation of light to form real, inverted, diminished, and colorful images.

Reflection of Light

When light falls on a mirror, it changes direction, which is called reflection of light.

• Laws of Reflection:
  1. The angle of incidence is equal to the angle of reflection,  Angle i =  Angle r .
  2. The incident ray, the reflected ray, and the normal to the surface lie in the same plane.
• Shadows are formed when opaque objects obstruct light sources.
• Solar and lunar eclipses are examples of the formation of shadows.

Refraction of Light

When a beam of light encounters another transparent medium, a part of light gets reflected back into the first medium and the rest enters the other medium. The direction of propagation of an incident ray of light that enters the other medium changes; this phenomenon is called refraction of light.

Laws of Refraction of Light

1. The incident ray, the refracted ray, and the normal to the interface at the point of incidence, all lie in the same plane.
2. The ratio of the sine of the angle of incidence (sin i) to the sine of the angle of refraction (sin r) is a constant, called the refractive index of the medium. i.e. 

Images

If light rays coming from a point after reflection meet at another point or appear to meet at another point, then the second point is called the image of the first point.

Types of Images

• Real Image: Always inverted and formed on the same side of the mirror. Real images can be obtained on a screen.
• Virtual Image: Always erect and formed behind the mirror. Virtual images cannot be obtained on a screen.

Comparison between Real and Virtual Images

Mirror

A mirror is a polished surface like glass, which reflects almost all the light that is incident on it. Mirrors are of two types:

Types of Mirrors

1. Plane Mirror: Has a flat reflecting surface.
2. 
   
   • Properties of Image formed by a Plane Mirror:
   • 
     
     • Virtual and erect.
     • Same size as the object.
     • Formed as far behind the mirror as the object is in front of it.
     • Laterally inverted (left appears right and vice versa).
3. Spherical Mirror: Has a curved reflecting surface.
4. 
   
   • Spherical mirrors are of two types:
   • 
     
     • Convex Mirror: Outward curved reflecting surface; diverges light rays.
     • Concave Mirror: Inward curved reflecting surface; converges light rays.

Formation of Image by Concave Mirror for Different Positions of Object

Dispersion of Light

The phenomenon of splitting white light into its component colors when passing through a prism is called dispersion of light. Red light is deviated the least, and violet light is deviated the most.

Cause of Dispersion

Light rays of different colors travel with the same speed in a vacuum and air, but in other media, they travel at different speeds and bend at different angles, leading to dispersion. Red light has the maximum wavelength and violet light has the minimum wavelength, so in any medium, red light travels the fastest and deviates the least, while violet light travels the slowest and deviates the most.

Wavelength ∝ Velocity ∝ 1/Deviation

Human Eye

The human eye is a complex optical instrument with a spherical shape. It can refract light to produce a focused image that stimulates a neural response, enabling us to see.

Important Parts of the Eye

1. Cornea: A transparent covering in the front of the eyeball that refracts light and protects the eye.
2. Iris: The dark muscular structure behind the cornea that controls the amount of light entering the eye by adjusting the size of the pupil and defines eye color.
3. Sclera: An opaque, fibrous, protective outer layer of the eye.
4. Ciliary Muscles: These hold the lens in position and help in focusing by modifying the curvature of the lens.
5. Crystalline Lens: A convex lens made of transparent, flexible, jelly-like proteins.
6. Pupil: A small opening in the middle of the eyeball, appearing as the black portion.
7. Retina: The inner surface of the eye, containing rods and cones. Cones are sensitive to bright light, while rods are sensitive to dim light but do not sense color.
8. Blind Spot: At the junction of the optic nerve and the retina, where there are no sensory cells, resulting in no vision at that spot.

Defects of Vision

1. Myopia (Nearsightedness): A condition where nearby objects are seen clearly, but far away objects are not. Corrected using concave lenses.
2. Hypermetropia (Farsightedness): A condition where far away objects are seen clearly, but nearby objects are not. Corrected using convex lenses.
3. Cataract: A condition in old age where eyesight becomes foggy. It is the most common cause of vision loss in people over 40 and can be treated.
4. Astigmatism: A vision condition where the cornea is not symmetrical, causing improper curvature. Corrected with glasses, contact lenses, refractive laser surgery, and implantable contact lenses. The contact lens for astigmatism is called toric.

Other Optical Instruments

• Telescope: Used to see distant objects distinctly.
• Microscope: Used to see very minute objects like cells and bacteria.
• Periscope: Used to see objects not in the direct line of sight.

Sound Energy

Sound is produced by vibrating objects. It cannot travel in a vacuum and needs a medium (gas, liquid, or solid) for propagation. Sound waves are longitudinal and travel in the form of compressions and rarefactions caused by the back-and-forth motion of the medium's particles.

Propagation of Sound

• The speed of sound waves depends on the elastic and inertia properties of the medium.
• Sound travels faster in solids than in liquids, and faster in liquids than in gases.

Terms Related to Sound Waves

• Amplitude: The maximum distance a vibrating body moves from its mean position.
• Time Period (T): The time taken to complete one oscillation. \( T ∝ 1/\nu \)
• Frequency: The number of oscillations per second, measured in Hertz (Hz).
• Like light, sound can be reflected, refracted, and diffracted, but it cannot be polarized.
• Wavelength (λ): The distance between two nearest particles of the medium vibrating in the same phase.
• Wave Velocity (v): The distance covered by a wave per unit time in its direction of propagation.

Wave Properties

The relationship between wave velocity, frequency, and wavelength is given by the equation:

Wave velocity (v) = Frequency (n) × Wavelength (λ)

In other terms, v = nλ where n = 1/λ.

How We Speak?

Humans produce sound using an organ called the voice box or larynx, located at the upper end of the windpipe. Two vocal cords are stretched across the voice box, leaving a narrow slit for air to pass through, producing sound.

How We Hear?

Sound enters our ear and travels down a canal to a thin membrane called the eardrum. The vibrations of the eardrum are transmitted to the inner ear and then to the brain as signals.

Characteristics of Sound

The way sound is perceived by the human ear is characterized by the following parameters:

• Pitch: Pitch depends on frequency. Higher frequency sounds have a higher pitch, while lower frequency sounds have a lower pitch.
• Loudness: Loudness depends on the intensity of the sound and is proportional to the square of the amplitude of vibration.
• Intensity: Intensity is defined as the amount of energy passing per unit area per unit time. Its SI unit is watt per meter (W/m²).
• Quality (Timbre): Quality is the characteristic that allows us to distinguish between sounds of the same pitch and loudness but produced by different sources. It depends on harmonics and their relative intensities.

Additional Facts About Sound

• Loudness Measurement: Loudness is measured in decibels (dB).
• Audible Range: Humans can hear frequencies between 20 Hz and 20 kHz. Sounds within this range are called audible sounds. Sounds below 20 Hz are infrasonic, and those above 20 kHz are ultrasonic.
• SONAR: SONAR (Sound Navigation and Ranging) uses ultrasonic waves and their reflection to locate objects underwater. It is used to measure distance, direction, and velocity of objects in water.
• Supersonic Speed: When an object moves faster than the speed of sound in air, it is said to have supersonic speed. Aircraft traveling at this speed are called supersonic aircraft.
• Echo: Echo is the phenomenon of sound reflection, resulting in the repetition of the sound. This occurs when sound waves bounce off a large obstacle.