Work and Energy – Class 9 CBSE Notes
Welcome to the notes on Work and Energy. In this chapter, we explore the concepts of work, energy, power, and their real-life applications. Let’s make learning easy and fun!
1. What is Work?
Work is said to be done when a force is applied to an object, and the object moves in the direction of the force. If there is no movement or displacement, no work is done.
Formula: W = F × d × cosθ
- W: Work done (Joules)
- F: Force applied (Newtons)
- d: Displacement of the object (meters)
- θ: Angle between force and displacement
Key Points:
- If
θ = 0°, work is maximum ascosθ = 1. - If
θ = 90°, no work is done ascosθ = 0.
2. Types of Work
Work can be of three types based on the direction of force and displacement:
- Positive Work: Force and displacement are in the same direction (e.g., lifting an object upwards).
- Negative Work: Force and displacement are in opposite directions (e.g., friction stopping a moving object).
- Zero Work: No displacement occurs, or force is perpendicular to displacement (e.g., holding a book stationary).
3. What is Energy?
Energy is the capacity to do work. It exists in various forms and can be transferred or converted from one form to another.
Unit: Joule (J)
Types of Energy
- Kinetic Energy (KE): Energy possessed by a moving object. Formula:
KE = ½ mv² - m: Mass of the object (kg)
- v: Velocity of the object (m/s)
- Potential Energy (PE): Energy possessed by an object due to its position or configuration. Formula:
PE = mgh - m: Mass of the object (kg)
- g: Acceleration due to gravity (9.8 m/s²)
- h: Height above the reference point (m)
4. Work-Energy Theorem
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
Formula: W = ΔKE = KEfinal - KEinitial
5. Power
Power is the rate of doing work or transferring energy.
Formula: P = W / t
- P: Power (Watts)
- W: Work done (Joules)
- t: Time taken (seconds)
Unit: Watt (W) where 1 W = 1 J/s
6. Commercial Unit of Energy
In everyday life, energy is measured in kilowatt-hours (kWh).
- 1 kWh = 1000 Watt × 1 hour = 3.6 × 106 Joules
- Used for billing electricity consumption in households.
7. Law of Conservation of Energy
Energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy in a system remains constant.
Example: In a pendulum, potential energy converts to kinetic energy and vice versa, but the total energy remains the same.
8. Applications of Work and Energy
- Understanding motion and forces in daily life.
- Designing energy-efficient machines and systems.
- Producing and conserving energy for sustainability.
Conclusion
Work and energy are fundamental concepts in physics that explain the interactions between forces and motion. Understanding these concepts helps us develop better technologies and appreciate the workings of the natural world.
Derivations of All Key Formulas – Work and Energy Class 9 CBSE
In this section, we will cover the derivation of all the important formulas from the chapter Work and Energy. Understanding these derivations will help you get a clear grasp of the concepts and prepare effectively for exams.
1. Derivation of Work Formula: W = F × d × cosθ
Work is said to be done when a force acts on an object and the object moves in the direction of the force. The formula for work is:
Work (W) = Force (F) × Displacement (d) × cos(θ)
Explanation:
When a force is applied at an angle θ to the direction of displacement, only the component of the force in the direction of displacement contributes to the work done. This is why we use the cosine of the angle between the force and displacement vector.
Steps for Derivation:
- Work is defined as the product of force and displacement:
W = F × d - If the force is applied at an angle θ with the direction of displacement, the effective force in the direction of displacement is
F × cos(θ). - Thus, the work done is:
W = F × d × cos(θ).
2. Derivation of Kinetic Energy Formula: KE = ½ mv²
Kinetic energy is the energy possessed by an object due to its motion. The formula for kinetic energy is derived from the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
Work-Energy Theorem: Work done (W) = Change in Kinetic Energy (ΔKE)
Steps for Derivation:
- Suppose an object of mass
mis initially at rest (u = 0) and is acted upon by a force that accelerates it to a final velocityv. - The work done by the force on the object is given by
W = F × d. - Using Newton’s second law,
F = ma(whereais acceleration), and the equation of motionv² = u² + 2ad(since initial velocity, u = 0), we get: d = v² / (2a)- Substituting this displacement value in the work equation:
W = ma × (v² / 2a) = ½ mv²- According to the work-energy theorem, the work done is equal to the change in kinetic energy. Since the object starts from rest,
KE = ½ mv².
3. Derivation of Potential Energy Formula: PE = mgh
Potential energy is the energy possessed by an object due to its position in a gravitational field. The formula for gravitational potential energy is derived based on the work done in lifting an object to a height.
Steps for Derivation:
- When an object of mass
mis lifted to a heighth, the work done against gravity is: Work = Force × Displacement- Here, the force required to lift the object is equal to its weight, which is
mg(wheregis the acceleration due to gravity). - The displacement is the height
hthrough which the object is lifted. - The work done to lift the object is:
Work = mg × h- This work done in lifting the object is stored as potential energy, so:
- PE = mgh
4. Derivation of Power Formula: P = W / t
Power is the rate at which work is done or energy is transferred. The formula for power is derived as follows:
Definition of Power: Power is the rate of doing work, i.e., how much work is done per unit time.
Steps for Derivation:
- Power is defined as the amount of work done per unit time:
P = W / t - Where
Pis power,Wis work done, andtis the time taken. - Therefore, the formula for power is: Power = Work / Time
5. Commercial Unit of Energy: 1 kWh = 3.6 × 106 J
Energy is commonly measured in kilowatt-hours (kWh) for electrical energy. The commercial unit of energy is derived as follows:
Steps for Derivation:
- 1 kWh represents the energy consumed by a 1-kilowatt device running for 1 hour.
- Power = 1 kW = 1000 W
- Time = 1 hour = 3600 seconds
- Energy (E) = Power × Time = 1000 W × 3600 s = 3.6 × 106 J
- Therefore, 1 kWh = 3.6 × 106 Joules.
Conclusion
In this section, we have derived the key formulas related to work, energy, power, and their applications. Understanding these derivations is essential for grasping the concepts of energy transformations, and they are important for solving both theoretical and numerical problems in exams.
Make sure to practice these derivations and understand the reasoning behind each formula for better exam preparation!
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