Class 9 Science Chapter 11 Work and Energy

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Class 9 Work and Energy Notes

This chapter explains the concepts of work, energy and power in physics. Work is said to be done when a force causes displacement. Energy is the ability or capacity to do work, and exists in forms like kinetic and potential energy. 

The chapter also introduces the work-energy theorem and the law of conservation of energy, which states that energy can neither be created nor destroyed. Let us now get into the detailed notes of this chapter.

Introduction to Work

Work is said to be done when a force is applied on an object and it produces displacement in the direction of the force. If there is no displacement, even if force is applied, no work is done. 

The amount of work done depends on three factors: the magnitude of the force, the displacement of the object and the angle between them. The formula for work is:

Work (W) = Force (F) x Displacement (d) x cos θ, where:

• F = force applied
• d = displacement of object
• θ = angle between force and displacement

Special Cases:

• If θ=0^∘: W = F × d (Maximum Work)
• If θ=90^∘: W = 0 (No Work)
  
• If θ=180^∘: W = −F × d (Negative Work)

Positive, Negative and Zero Work

• Positive Work: Force and displacement in the same direction (e.g., pushing a box forward).
• Negative Work: Force and displacement in opposite directions (e.g., friction).
• Zero Work: No displacement or force is perpendicular to displacement (e.g., carrying a bag while walking).

What is Energy?

Energy is defined as the capacity to do work. It is a scalar quantity, which means it has magnitude but no direction. The SI unit of energy is the Joule (J). 

Energy comes in various forms such as kinetic energy, potential energy, heat energy, light energy, chemical energy, etc. In this chapter, we mainly focus on mechanical energy (kinetic and potential).

1. Kinetic Energy (KE)

Kinetic energy is the energy possessed by a body due to its motion. Any moving object, whether a ball, a car and a person running has kinetic energy. The faster it moves, the more kinetic energy it has. The formula for kinetic energy is:

KE = ½ mv²

Where:

• m = mass of the object (kg)
• v = velocity of the object (m/s)

2. Potential Energy (PE)

Potential energy is the energy possessed by a body due to its position or configuration. For example, an object placed at a height has potential energy due to gravity. When it falls, this energy gets converted to kinetic energy. 

The formula for gravitational potential energy is:

PE =  mgh

Where:

• m = mass (kg)
• g = acceleration due to gravity (9.8 m/s²)
• h = height (m)

Work-Energy Theorem

The work-energy theorem states that the work done by a force on an object is equal to the change in its kinetic energy. This means if an object speeds up, work has been done on it and if it slows down, work is done by it. 

Mathematically,

Work done = Change in kinetic energy, or

W = KE_final − KE_initial, or

W = ½ m(v² - u²)

Law of Conservation of Energy

This law says that energy can neither be created nor destroyed. It can only be changed from one form to another. The total energy of an isolated system always remains constant. 

For example, when a ball falls from a height:

• At the top: Only PE
• Midway: PE + KE
• Just before hitting the ground: Maximum KE, minimum PE
• Total Energy = Constant

Commercial Unit of Energy (Joule)

While the SI unit of energy is the Joule, in homes and industries, we use a larger unit called the kilowatt-hour (kWh).

1 kWh = 1000 W × 3600 s = 3.6×10⁶ J

This is the unit seen on electricity bills, where 1 kWh means 1 kilowatt of power used for 1 hour.

What is Power?

Power is defined as the rate at which work is done or energy is consumed. It tells us how fast or slow work is being done. The formula for power is:

Power (P) = Work done (W) / Time (t)

Its SI unit is the watt (W). One watt is the power when one joule of work is done in one second. Bigger units like kilowatt (kW) and megawatt (MW) are used for large-scale energy use. 

1 Watt = 1 Joule / 1 Second

Other units:

• 1 kilowatt (kW) = 1000 W
• 1 megawatt (MW) = 10⁶ W

Average Power

Sometimes, work is done at varying rates. In such cases, we calculate average power using the formula:

Average Power = Total Work Done / Total Time Taken

NOTE: Power at a particular instant is called instantaneous power.

This gives us an overall idea of the rate at which energy is consumed or work is done over a period.

Some Important Numerical Qs

1. A force of 10 N is applied on a body and it moves a distance of 5 meters in the direction of the force. Calculate the work done.

Solution: W = F x d = 10 x 5 = 50 Joules

2. A person applies a force of 20 N on a box, but the box moves 2 m in the opposite direction. Calculate the work done. 

Solution: W = F x d x cos180° = 20 x 2 x (-1) = -40 J

3. A coolie lifts a suitcase and walks 10 m on a flat surface. The suitcase is lifted vertically upward but displacement is horizontal. Calculate the work done by the coolie.

Solution: W = f x d x cos90° = 0 

4. Calculate the kinetic energy of a body of mass 2 kg moving with a velocity of 3 m/s.

Solution: KE = ½ mv² = ½ x 2 x 3 x 3 = 1 x 9 = 9 J

5. An object of mass 10 kg is raised to a height of 5 m. Find its potential energy.

Solution: PE = m g h = 10 x 9.8 x 5 = 490 J

6. A person does 1200 J of work in 2 minutes. What is the average power?

Solution: P = W / t = 1200 / 120 = 10W

FAQs

Q1. What is meant by “work” in science?

Ans. Work is done when a force is applied on an object and the object gets displaced in the direction of force.

Q2. When is work said to be positive or negative?

Ans. Positive work is when force and displacement are in the same direction (e.g., pushing a moving car). Negative work is when force and displacement are opposite (e.g., friction on a moving object).

Q3. What is the Work-Energy Theorem?

Ans. It states that the work done on an object is equal to the change in its kinetic energy.

Q4. What is the law of conservation of energy?

Ans. Energy can neither be created nor destroyed; it only changes from one form to another and the total energy remains constant.

Q5. What are the main forms of mechanical energy?

Ans. Kinetic Energy (KE) is the energy due to motion and Potential Energy (PE) is the energy due to position or configuration.