Work and energy

Work

Work is said to be done , if on applying a force on an object, it is displaced from its position in the direction of force .

In physics, work done is a specific measure of energy transfer. It isn’t just “effort”—you can push against a wall until you’re exhausted, but if the wall doesn’t move, you’ve done zero work in the eyes of physics.

Two conditions to satisfy for work done:-

• A force should act an an object.
• The object must be displaced.

Work and energy

Atom: Building Blocks of the Universe

The Basic Formula

If you apply a constant force to an object and it moves in a straight line, the work done (W) is the product of the force (F) and the displacement (d) in the direction of that force.

• W: Work done (measured in Joules, J).

• F: Magnitude of the force (measured in Newtons, N).

• d: Displacement (measured in meters, m).

• θ: The angle between the force and the direction of motion.

• Unit: 1 Joule (J) = 1 Newton (N) ×meter (m).

Three Types of Work

The value of work depends heavily on the direction you are pushing vs. the direction the object is moving.

Work Done by Variable Forces

In the real world, forces aren’t always constant (like stretching a spring—the harder you pull, the more resistance you feel). In these cases, we use calculus to sum up all the tiny bits of work.

 The Work-Energy Theorem

This is one of the most important connections in physics. It states that the net work done on an object is equal to its change in Kinetic Energy (K)

Essentially, if you do positive work on an object, you are “depositing” energy into it, causing it to speed up. If you do negative work, you are “withdrawing” energy, causing it to slow down.

Energy

Energy is the capacity to do work. An object that does work loses energy, while the object on which work is done gains energy.

♦Types of energy:-

Mechanical energy:-

To understand Mechanical Energy, we look at the two forms that define an object’s physical state: Kinetic Energy (the energy of motion) and Potential Energy (the energy of position).

1. Kinetic Energy (KE)

Kinetic energy is the energy possessed by an object due to its motion. Any object that has mass and is moving at any speed possesses kinetic energy.

• Factors: It depends on the mass (m) of the object and its velocity (v).

• Formula Derivation:Suppose an object of mass m is at rest (u = 0).A force (F) is applied, giving it an acceleration (a) over a distance (s) until it reaches velocity (v).

  1. Work done: W = F × s

  2. From Newton’s second law: F = ma

  3. From the third equation of motion: v² = u² + 2as  => s = (v² – u²) / 2a

  4. Substitute F and s into the work formula:
     KE = ½mv²

     This work done is stored as Kinetic Energy (KE).

2. Potential Energy (PE)

Potential energy is the energy stored in an object because of its position or configuration (shape).

Gravitational Potential Energy

This is the most common type discussed in Class 9. It is the energy an object gains when it is lifted against gravity.

• Formula: PE = mgh

  • m = mass

  • g = acceleration due to gravity (9.8 m/s)

  • h = height above a reference point (usually the ground).

Elastic Potential Energy

Energy stored when an object is deformed, like a stretched rubber band or a compressed spring. When you let go, this stored energy converts back into kinetic energy.

Energy Transformation (Inter-conversion)

Energy rarely stays in one form.The process of changing from one form to another is called Energy Transformation.

Common Examples of Transformations:

Law of Conservation of Energy: A Closer Look

According to this law, while energy changes form, the Total Energy of an isolated system remains constant.

For example, when a ball is dropped from a height (h):

1. At height (h): It has maximum Potential Energy (PE) and zero Kinetic Energy.

2. During the fall: PE decreases (as height decreases) and KE increases (as speed increases).

3. Just before hitting the ground: PE becomes zero, and all of it has transformed into maximum Kinetic Energy (KE).

4. The sum (PE + KE) is the same at every single point during the fall.

Understanding the Commercial Unit

Since the Joule (J) is a very small unit, we use the Kilowatt-hour (kWh) for commercial purposes like home electricity bills.

• 1 kWh = 1 unit of electricity.

• 1 kWh = 3.6× 10^6 Joules.

Power

Power is often described as the “speed” of work.  While work tells us how much energy was used, power tells us how fast it was used.

1. Definition and Formula

Power is the rate of doing work or the rate of transfer of energy.

• Formula: P = w/t

  • P = Power

  • W = Work done (or Energy consumed)

  • t = Time taken

• The Velocity Relation: Power can also be expressed in terms of force and speed:P = F× v

2. Units of Power

• S.I. Unit: The Watt (W), named after James Watt.

  • 1 Watt: The power of an agent which does work at the rate of 1 Joule per second (1W = 1J/s).

• Higher Units: 1Kilowatt (kW) = 1000W.

  • 1 Megawatt (MW) = 10^6W

  • 1 Horsepower (hp) = 746W (commonly used for car engines and water pumps).

3. Average Power

In real life, the rate of doing work may change over time. For example, a runner might start fast and slow down. In such cases, we calculate Average Power:

Average Power = Total work done/Total time taken

4. Kilowatt vs. Kilowatt-hour (The Big Confusion)

Students often confuse these two, but they measure completely different things:

Conversion Tip:1kWh = 1000W ×  3600 s = 3.6×10^6 Joules.

Work and energy