Work and Energy Class 9 Chapter Notes (Science)

Key Formulas & Concepts

• Work Done (W): Work is done when a force (F) produces a displacement (s) in an object. Formula: W = F × s × cos(θ), where θ is the angle between the force and displacement vectors.
• SI Unit of Work & Energy: The SI unit for both work and energy is the Joule (J). 1 Joule is the work done when a force of 1 Newton displaces an object by 1 meter.
• Types of Work: Work can be positive (force and displacement in the same direction, θ=0°), negative (force and displacement in opposite directions, θ=180°), or zero (force is perpendicular to displacement, θ=90°, or displacement is zero).
• Kinetic Energy (K.E.): The energy possessed by an object due to its motion. Formula: K.E. = ½ mv².
• Potential Energy (P.E.): The energy possessed by an object due to its position or configuration. For an object at height 'h', Formula: P.E. = mgh.
• Law of Conservation of Energy: Energy can only be transformed from one form to another; it cannot be created or destroyed. The total energy of an isolated system remains constant. (P.E. + K.E.)_initial = (P.E. + K.E.)_final.
• Power (P): The rate at which work is done or energy is transferred. Formula: P = W/t or P = E/t.
• SI Unit of Power: The SI unit of power is the Watt (W). 1 Watt is the power of an agent doing 1 Joule of work in 1 second.
• Commercial Unit of Energy: The commercial unit of electrical energy is the kilowatt-hour (kWh). 1 kWh is also known as '1 unit'.
• Conversion: 1 kWh = 3.6 × 10⁶ J.

Key Terms and Definitions

Work

In physics, work is done on an object when an applied force causes a displacement of the object in the direction of the force component.

Joule (J)

The SI unit of work and energy. One joule is defined as the amount of work done when a force of one newton displaces an object by one meter.

Energy

The capacity or ability to do work. It exists in various forms, such as kinetic, potential, heat, and chemical energy.

Kinetic Energy

The energy an object possesses due to its motion. It depends on the mass and the square of the velocity of the object.

Potential Energy

The stored energy an object has because of its position or state. Gravitational potential energy is a common example.

Power

The rate at which work is done or the rate at which energy is transferred or converted. It measures how fast work is performed.

Watt (W)

The SI unit of power. One watt is equal to one joule of work done per second (1 J/s).

Law of Conservation of Energy

A fundamental principle stating that the total energy of an isolated system remains constant over time. Energy is conserved, it only changes form.

Kilowatt-hour (kWh)

A commercial unit of energy, commonly used for electricity bills. It is the energy consumed by a 1-kilowatt device operating for one hour.

Understanding the Work-Energy Theorem

A core concept in this chapter is the direct relationship between work and energy, formalized by the Work-Energy Theorem. This theorem states that the net work done on an object is equal to the change in its kinetic energy.

Mathematically, W_net = ΔK.E. = K.E._final - K.E._initial.

Let's break this down. When you apply a net force to an object and cause it to move, you are doing work on it. This work transfers energy to the object, causing its speed, and therefore its kinetic energy, to change.

• If you push a stationary car, you do positive work, and its kinetic energy increases from zero. The work you did is converted into the car's kinetic energy.
• If a moving car applies brakes, the force of friction does negative work on the car. This removes kinetic energy from the car (converting it mostly to heat), causing it to slow down.

The theorem also connects to potential energy. When you lift a book from the floor to a shelf, you do work against gravity. This work is stored in the book as gravitational potential energy. If the book falls, this potential energy is converted back into kinetic energy. The total mechanical energy (Potential + Kinetic) remains constant if we ignore air resistance, which is a demonstration of the Law of Conservation of Energy.

Positive, Negative, and Zero Work

Quick Numerical Examples

• {"title":"Calculating Work Done","problem":"A force of 10 N is applied to a box, which moves a distance of 5 m in the direction of the force. Calculate the work done.","solution":"Given: Force (F) = 10 N, Displacement (s) = 5 m, Angle (θ) = 0° (since direction is same).\nWork Done (W) = F × s × cos(0°)\nW = 10 N × 5 m × 1\nW = 50 J"}
• {"title":"Calculating Kinetic Energy","problem":"Calculate the kinetic energy of a car of mass 1000 kg moving with a velocity of 20 m/s.","solution":"Given: Mass (m) = 1000 kg, Velocity (v) = 20 m/s.\nKinetic Energy (K.E.) = ½ mv²\nK.E. = ½ × 1000 kg × (20 m/s)²\nK.E. = 500 × 400\nK.E. = 200,000 J or 200 kJ"}
• {"title":"Calculating Power","problem":"An electric motor lifts a 50 kg load to a height of 10 m in 5 seconds. Calculate the power of the motor. (g = 10 m/s²)","solution":"First, calculate the work done (which is equal to the potential energy gained).\nWork Done (W) = P.E. = mgh\nW = 50 kg × 10 m/s² × 10 m = 5000 J.\nTime (t) = 5 s.\nPower (P) = Work / Time\nP = 5000 J / 5 s\nP = 1000 W or 1 kW"}

Common Exam Mistakes

Be careful with the definition of 'work' in physics vs. daily life. Studying for hours is hard work, but in physics, if there's no displacement, no work is done. Also, always check the angle between force and displacement. If a force is perpendicular to displacement (like gravity on an object moving horizontally), the work done by that specific force is zero. For numericals, ensure all units are in the SI system (mass in kg, velocity in m/s, distance in m) before applying formulas. A common trap is giving mass in grams or velocity in km/hr.

Practice Questions with Solutions

• Q: What is the commercial unit of energy and how is it related to its SI unit? A: The commercial unit of energy is the kilowatt-hour (kWh). 1 kWh is the energy used by a 1 kW appliance in 1 hour. Its relation to the SI unit (Joule) is: 1 kWh = 3.6 × 10⁶ J.
• Q: Give two conditions under which work done is zero. A: Work done is zero when: 1. There is no displacement (s=0), e.g., pushing against a wall. 2. The applied force is perpendicular to the direction of displacement (θ=90°), e.g., a satellite orbiting the Earth.
• Q: An object of mass 'm' is moving with a velocity 'v'. How much work is needed to bring it to rest? A: According to the work-energy theorem, the work done is equal to the change in kinetic energy. To bring it to rest, the final K.E. is 0. So, Work Done = 0 - (½ mv²) = -½ mv². The work done is negative, equal in magnitude to its initial kinetic energy.
• Q: A freely falling body eventually stops on hitting the ground. What happens to its kinetic energy? A: When the body hits the ground, its kinetic energy is converted into other forms of energy, primarily heat energy (due to the inelastic collision with the ground) and sound energy.

Frequently Asked Questions

Frequently Asked Questions