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9th Physics Federal Board Notes: Unit 6 - Work and Energy
📋 Table of Contents
- 1. Multiple Choice Questions
- 2. Short Response Questions
- 2.1 Work Done on a Moving Car
- 2.2 Work in Raising a Box
- 2.3 Work by Centripetal Force
- 2.4 Kinetic Energy Change with Velocity
- 2.5 Energy Conversion in Bullet Penetration
- 2.6 Efficiency and Energy Conservation
- 2.7 Renewable vs Non-renewable Energy
- 2.8 Future of Renewable Energy
- 2.9 Power and Energy Consumption
- 2.10 Perpetual Engine Efficiency
- 3. Long Response Questions
- 3.1 Definition of Work and Conditions
- 3.2 Kinetic Energy and Derivation
- 3.3 Potential Energy and Types
- 3.4 Energy Conversion and Conservation
- 3.5 Energy from Natural Resources
- 3.6 Renewable vs Non-renewable Energy
- 3.7 Energy Conversion Processes
- 3.8 Electricity Generation from Fossil Fuels
- 3.9 Power and Horsepower
- 3.10 Efficiency and Its Importance
- 3.11 Energy Flow Diagrams
🔬 Introduction to Unit 6: Work and Energy
Unit 6: Work and Energy explores the fundamental concepts of work, energy, and power in physics. This unit helps students understand how energy is transferred, transformed, and conserved in various systems. You'll learn about different forms of energy, the relationship between work and energy, power calculations, and the importance of energy sources in our daily lives.
Multiple Choice Questions
One joule is equal to one watt-second, as power (watt) multiplied by time (second) gives energy (joule).
Since kinetic energy \( E_k = \frac{1}{2}mv^2 \), for the same kinetic energy, the object with the smallest mass will have the highest speed.
Potential energy \( E_p = mgh = weight \times height = 50 \times 5 = 250 \) J.
Power \( P = \frac{W}{t} = \frac{100}{5} = 20 \) W.
The SI unit of power is the watt (W), named after James Watt.
Initial kinetic energy \( E_k = \frac{1}{2}mv^2 = \frac{1}{2} \times 4 \times (5)^2 = 50 \) J. Due to conservation of energy, it will have the same kinetic energy when it returns to the starting point.
As the ball falls downward, its height decreases (decreasing potential energy) while its speed increases (increasing kinetic energy).
Geothermal energy comes from the natural heat within the Earth, including heated groundwater.
Power \( P = \frac{W}{t} = \frac{mgh}{t} \)
\( 1960 = \frac{M \times 9.8 \times 2}{3} \)
\( M = \frac{1960 \times 3}{9.8 \times 2} = 300 \) kg
Sunlight is a renewable energy source as it is continuously available and naturally replenished.
1 horsepower (hp) is approximately equal to 746 watts.
Due to energy losses (mainly as heat), no practical engine can achieve 100% efficiency (efficiency = 1).
Since momentum \( p = mv \) and kinetic energy \( E_k = \frac{p^2}{2m} \), for the same momentum, the lighter object will have greater kinetic energy.
Work \( W = F \cdot d \cdot \cos\theta \). If displacement \( d = 0 \), then work done is zero.
The work done in lifting the box increases its gravitational potential energy.
Short Response Questions
1. A car is moving with a constant speed along a straight road. Is there any work done on the car?
No, there is no net work done on the car while it moves with constant speed along a straight road. According to the work-energy principle, work is done only when there is a change in kinetic energy. Since the car's speed remains constant, its kinetic energy doesn't change, and therefore no net work is being done on it. The engine does work to overcome friction and air resistance, but this work is balanced by the dissipative forces, resulting in zero net work.
2. Does the work done in raising a box up in a building depend upon how fast it is raised up? Through which path? To how much height?
The work done in raising a box depends only on the height it is lifted, not on how fast it is raised or the specific path taken. This is because gravitational potential energy depends only on the vertical displacement:
Where:
- \( m \) = mass of the box
- \( g \) = acceleration due to gravity
- \( h \) = height lifted
The speed of lifting affects the power required (work per unit time) but not the total work done. Similarly, the path taken (straight up, zigzag, etc.) doesn't change the work as long as the final height is the same.
3. Work done on the body either speeds it up, slows it down. Keeping it mind, explain how much work is done by centripetal force on an orbiting satellite?
Centripetal force does zero work on an orbiting satellite. This is because:
- Work is defined as \( W = F \cdot d \cdot \cos\theta \), where \( \theta \) is the angle between force and displacement
- In circular motion, centripetal force always acts perpendicular to the direction of motion (toward the center)
- When force is perpendicular to displacement, \( \theta = 90^\circ \) and \( \cos 90^\circ = 0 \)
- Therefore, \( W = F \cdot d \cdot 0 = 0 \)
The centripetal force changes the direction of the satellite's velocity but not its speed, so the kinetic energy remains constant, confirming that no work is done.
4. A car has Kinetic energy \( E_{k} \). By what factor its kinetic energy would change, if its velocity is doubled?
If the car's velocity is doubled, its kinetic energy increases by a factor of four. This relationship comes from the kinetic energy formula:
When velocity becomes \( 2v \):
Thus, doubling the velocity quadruples the kinetic energy.
5. A bullet is fired from gun, bullet penetrates into sand wall and it stops. Where does its kinetic energy used?
When a bullet penetrates a sand wall and stops, its kinetic energy is transformed into other forms of energy:
- Heat energy: The majority of kinetic energy converts to heat due to friction between the bullet and sand particles
- Sound energy: Some energy is converted to sound during impact and penetration
- Deformation energy: Energy is used to deform both the bullet and the sand particles
- Potential energy: A small amount may be stored as potential energy in the compressed sand
This transformation follows the law of conservation of energy - the total energy before and after penetration remains constant, just in different forms.
6. An LED light bulb has efficiency of 80%. Does it violate conservation of energy principle?
No, an LED light bulb with 80% efficiency does not violate the conservation of energy principle. The principle states that energy cannot be created or destroyed, only transformed from one form to another.
In the LED bulb:
- 80% of electrical energy converts to light energy
- 20% converts to heat energy
The total energy output (light + heat) equals the electrical energy input, satisfying conservation of energy. Efficiency below 100% simply means some energy is transformed into less useful forms, not that energy is lost.
7. How does using renewable energy sources contribute to sustainable development?
Using renewable energy sources contributes to sustainable development in several important ways:
- Environmental protection: Renewable sources like solar, wind, and hydro produce little to no greenhouse gases or pollution
- Resource conservation: They don't deplete finite resources like fossil fuels
- Energy security: Reduce dependence on imported fuels and price fluctuations
- Economic benefits: Create jobs in manufacturing, installation, and maintenance
- Long-term availability: Renewable sources are naturally replenished and won't run out
- Health benefits: Reduce air pollution-related diseases
This approach meets current energy needs without compromising the ability of future generations to meet their own needs.
8. What is the future of renewable energy in Pakistan?
The future of renewable energy in Pakistan is promising due to several factors:
- Abundant solar potential: Pakistan receives high solar radiation throughout the year, especially in Balochistan and Sindh
- Wind energy potential: Coastal areas of Sindh have excellent wind resources
- Hydropower capacity: Northern areas offer significant hydropower potential
- Government initiatives: Projects like the China-Pakistan Economic Corridor (CPEC) include renewable energy components
- Energy crisis solution: Renewables can help address Pakistan's chronic energy shortages
- Economic benefits: Reduced fuel imports and job creation in the renewable sector
With proper investment and policy support, renewable energy could play a major role in Pakistan's energy mix, contributing to energy security, economic growth, and environmental protection.
9. A 100 W light bulb is switched on for 10 hours. How much energy is consumed by it in kWh?
To calculate the energy consumption:
The bulb consumes 1 kilowatt-hour (kWh) of electrical energy. This is the standard unit for electricity billing.
10. Why can't we have an engine with 100% efficiency?
We cannot have an engine with 100% efficiency due to fundamental physical limitations:
- Second Law of Thermodynamics: Heat cannot be completely converted to work in a cyclic process
- Heat losses: Some energy is always lost as waste heat to the surroundings
- Friction: Mechanical systems always experience friction, converting some energy to heat
- Practical limitations: Real engines have imperfections in materials and design
The maximum possible efficiency for a heat engine is given by the Carnot efficiency:
Where \( T_c \) is the cold reservoir temperature and \( T_h \) is the hot reservoir temperature (in Kelvin). Since \( T_c \) is never absolute zero, efficiency can never reach 100%.
Long Response Questions
1. Define work and write down its formula. Give the conditions for positive, negative, and zero work done. Give one example of each.
Definition: Work is done when a force causes displacement of an object in the direction of the force component.
Formula: \( W = F \cdot d \cdot \cos\theta \)
Where:
- \( W \) = work done
- \( F \) = applied force
- \( d \) = displacement
- \( \theta \) = angle between force and displacement vectors
| Type of Work | Condition | Example |
|---|---|---|
| Positive Work | When force and displacement are in the same direction (\( 0^\circ \leq \theta < 90^\circ \)) | Pushing a box forward across a floor |
| Negative Work | When force and displacement are in opposite directions (\( 90^\circ < \theta \leq 180^\circ \)) | Applying brakes to slow down a moving car |
| Zero Work | When force and displacement are perpendicular (\( \theta = 90^\circ \)) or no displacement occurs | Carrying a heavy bag while walking horizontally |
2. Define kinetic energy. Derive the equation for kinetic energy \( E_k = \frac{1}{2}mv^2 \).
Definition: Kinetic energy is the energy possessed by an object due to its motion.
Derivation:
Consider an object of mass \( m \) initially at rest. A constant force \( F \) is applied to it, causing acceleration \( a \) and displacement \( d \).
From Newton's second law: \( F = ma \)
Work done on the object: \( W = F \cdot d = ma \cdot d \)
From equations of motion: \( v^2 = u^2 + 2ad \)
Since initial velocity \( u = 0 \): \( v^2 = 2ad \) or \( ad = \frac{v^2}{2} \)
Substituting: \( W = m \cdot \frac{v^2}{2} = \frac{1}{2}mv^2 \)
This work done is stored as kinetic energy: \( E_k = \frac{1}{2}mv^2 \)
3. Define potential energy. Write down the different types of potential energy with one example of each.
Definition: Potential energy is the energy stored in an object due to its position, configuration, or state.
Gravitational Potential Energy
Energy due to an object's height in a gravitational field.
Formula: \( E_p = mgh \)
Example: Water stored in a dam
Elastic Potential Energy
Energy stored in stretched or compressed elastic materials.
Formula: \( E_p = \frac{1}{2}kx^2 \)
Example: A stretched rubber band
Chemical Potential Energy
Energy stored in chemical bonds between atoms.
Example: Energy in food, batteries, or fuels
Nuclear Potential Energy
Energy stored in the nucleus of atoms.
Example: Energy in uranium used in nuclear power plants
Electric Potential Energy
Energy due to the position of charged particles in an electric field.
Example: Energy stored in capacitors
Magnetic Potential Energy
Energy due to the position of magnetic materials in a magnetic field.
Example: Energy stored when separating two magnets
4. State and explain the law of conservation of energy. Give two examples of energy conversion from daily life.
Law of Conservation of Energy: Energy cannot be created or destroyed; it can only be transformed from one form to another. The total energy in an isolated system remains constant.
Example 1: Pendulum
As a pendulum swings:
- At highest point: Maximum potential energy, zero kinetic energy
- At lowest point: Maximum kinetic energy, minimum potential energy
- Total energy remains constant (ignoring air resistance)
Example 2: Electric Heater
In an electric heater:
- Electrical energy → Heat energy
- Total energy before and after conversion remains the same
- Some energy may be lost as sound or light, but total is conserved
Other examples include:
- Solar cell: Light energy → Electrical energy
- Car engine: Chemical energy (fuel) → Heat → Kinetic energy
- Human body: Chemical energy (food) → Kinetic energy + Heat
5. What are the main sources of energy that we get from the natural environment? Also write down the names of devices which convert these energies into useful forms.
| Energy Source | Description | Conversion Devices |
|---|---|---|
| Solar Energy | Energy from the sun in the form of light and heat | Solar panels, solar water heaters, solar cells |
| Wind Energy | Kinetic energy of moving air | Wind turbines, windmills |
| Hydropower | Energy from flowing or falling water | Hydroelectric dams, water turbines |
| Geothermal Energy | Heat energy from within the Earth | Geothermal power plants, heat pumps |
| Biomass Energy | Energy from organic materials | Biogas plants, biomass power plants |
| Fossil Fuels | Chemical energy from ancient organic matter | Thermal power plants, internal combustion engines |
| Nuclear Energy | Energy stored in atomic nuclei | Nuclear reactors |
| Tidal Energy | Energy from ocean tides | Tidal barrages, tidal turbines |
6. Differentiate between renewable and non-renewable sources of energy. Give two examples of each.
| Aspect | Renewable Energy | Non-renewable Energy |
|---|---|---|
| Definition | Energy sources that are naturally replenished | Energy sources that cannot be replenished in human timescales |
| Availability | Virtually inexhaustible | Finite and depleting |
| Environmental Impact | Generally low pollution and greenhouse gases | High pollution and greenhouse gas emissions |
| Cost | High initial cost, low operating cost | Variable costs depending on availability |
| Examples | Solar, wind, hydropower, geothermal | Coal, oil, natural gas, nuclear fuels |
| Sustainability | Sustainable for future generations | Not sustainable in the long term |
Examples of Renewable Energy:
- Solar Energy: From sunlight using solar panels
- Wind Energy: From wind using wind turbines
Examples of Non-renewable Energy:
- Coal: Mined from the earth and burned for electricity
- Natural Gas: Extracted from underground reserves
7. Describe the process of energy conversion in the following cases: (a) Hydroelectric power station (b) Nuclear power station (c) Solar cell
(a) Hydroelectric Power Station
Energy Conversion Process:
- Potential energy of water stored at height
- → Kinetic energy of falling water
- → Mechanical energy in turbine rotation
- → Electrical energy in generator
Key Components: Dam, penstock, turbine, generator, transformer
(b) Nuclear Power Station
Energy Conversion Process:
- Nuclear potential energy in uranium atoms
- → Thermal energy from nuclear fission
- → Kinetic energy of steam
- → Mechanical energy in turbine rotation
- → Electrical energy in generator
Key Components: Reactor core, heat exchanger, turbine, generator
(c) Solar Cell
Energy Conversion Process:
- Radiant energy from sunlight
- → Electrical energy through photovoltaic effect
Key Components: Semiconductor material (usually silicon), electrodes
Note: This is a direct energy conversion without intermediate steps
8. How is electricity generated from fossil fuels in a thermal power station? Draw a block diagram.
Process of Electricity Generation from Fossil Fuels:
- Fuel Combustion: Fossil fuels (coal, oil, or natural gas) are burned in a boiler
- Heat Transfer: The heat produced converts water into high-pressure steam
- Mechanical Energy: Steam at high pressure turns the blades of a turbine
- Electrical Generation: The rotating turbine spins a generator to produce electricity
- Transmission: Electricity is stepped up in voltage and transmitted through power lines
- Cooling: Steam is condensed back to water and recycled
Block Diagram of Thermal Power Station:
Fuel Storage → Boiler → Steam Turbine → Generator → Transformer → Power Grid
↓
Condenser → Water Pump (back to boiler)
Efficiency Considerations: Typical thermal power plants have 30-40% efficiency due to heat losses in various stages of conversion.
9. Define power and write its formula. Also define horsepower.
Definition of Power: Power is the rate at which work is done or energy is transferred.
Formula: \( P = \frac{W}{t} \)
Where:
- \( P \) = power
- \( W \) = work done
- \( t \) = time taken
SI Unit: Watt (W), where 1 W = 1 J/s
🐎 Horsepower
Definition: Horsepower is a unit of power in the imperial system, originally developed to compare the output of steam engines with the power of draft horses.
Conversion: 1 horsepower (hp) = 746 watts
Historical Context: James Watt introduced this unit during the 18th century to help market his improved steam engine by comparing it to the number of horses it could replace.
10. Define efficiency. Why is it important? Write down its formula.
Definition: Efficiency is the ratio of useful energy output to the total energy input, expressed as a percentage.
Formula: \( \eta = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100\% \)
Importance of Efficiency:
- Resource Conservation: Higher efficiency means less fuel consumption for the same output
- Cost Savings: Reduced energy costs for consumers and businesses
- Environmental Protection: Lower emissions and pollution
- Energy Security: Reduced dependence on energy imports
- Sustainability: Extends the life of finite energy resources
- Economic Benefits: Lower operational costs and increased competitiveness
💡 Practical Tip
No system can be 100% efficient due to inevitable energy losses, mainly as heat. The theoretical maximum efficiency for heat engines is given by the Carnot efficiency formula.
11. Draw and explain the energy flow diagram for Pakistan.
Energy Flow Diagram for Pakistan:
Energy Sources (Input)
Non-renewable (≈65%):
- Natural Gas (≈35%)
- Oil (≈20%)
- Coal (≈8%)
- Nuclear (≈2%)
Renewable (≈35%):
- Hydropower (≈25%)
- Solar, Wind, Others (≈10%)
Conversion & Distribution
Power Generation: Thermal plants, hydroelectric dams, nuclear plants, renewable installations
Transmission: National grid through transmission lines
Distribution: To industrial, commercial, and residential consumers
Energy Consumption (Output)
Industrial Sector: ≈35%
Transportation: ≈30%
Residential: ≈25%
Commercial & Agriculture: ≈10%
Key Challenges in Pakistan's Energy Flow:
- High dependence on imported fossil fuels
- Transmission and distribution losses (≈15-20%)
- Seasonal variations in hydropower generation
- Growing energy demand outpacing supply
- Need for diversification to renewable sources
Future Directions: Increasing share of renewables, improving energy efficiency, reducing transmission losses, and exploring indigenous energy resources.
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