Work and Energy – CBSE NCERT Study Resources

In science, work is done when a force causes displacement in its direction. It is calculated as Work = Force × Displacement × cosθ.

Work is zero if displacement is zero or force is perpendicular to displacement. For example, pushing a wall doesn’t do work as there’s no displacement.

Our textbook shows a coolie carrying luggage horizontally—work done against gravity is zero since displacement is perpendicular to the force.

Kinetic energy is the energy possessed by a moving object. It depends on mass (m) and velocity (v).

We studied in NCERT how a rolling ball does work. Using Work = Force × Displacement and Newton’s laws, we integrate to derive KE = ½ mv².

A faster cricket ball has more KE, causing greater impact—just like in our textbook example.

Potential energy is stored energy due to position/stress, like a stretched spring or raised object.

Our textbook shows water in a dam has gravitational PE. Unlike kinetic energy (motion-based), PE depends on height (PE = mgh).

A bow stores elastic PE when drawn. When released, it converts to KE—just like NCERT’s archery example.

Energy cannot be created/destroyed—it only converts forms. Total energy remains constant.

In NCERT’s pendulum example, PE at the top converts to KE at the bottom. Friction aside, the sum stays the same.

A roller coaster mimics this: PE at the peak transforms into KE during the drop, just like our textbook explains.

Power is the rate of doing work (Power = Work/Time). It measures how fast energy is transferred.

Our textbook defines power using stairs. If both students do equal work (same height), the faster one has higher power as time is less.

Like a bulb’s wattage, higher power means quicker energy use—similar to NCERT’s electric appliances example.

Work is done when a force causes displacement in its direction. It is calculated as W = F × s × cosθ.

Our textbook shows lifting a book: work is done against gravity. If force or displacement is zero, no work is done.

Pushing a wall doesn’t do work as there’s no displacement, but pushing a cart does.

Potential energy is stored energy (e.g., height), while kinetic energy is due to motion.

NCERT shows a stretched bow (potential) and moving arrow (kinetic). Energy interconversion follows the law of conservation.

A roller coaster at the top has potential energy, which converts to kinetic as it descends.

Energy cannot be created or destroyed, only transformed. Total energy remains constant.

NCERT’s swinging pendulum shows kinetic ↔ potential energy conversion without loss.

In hydroelectric plants, water’s potential energy converts to electrical energy, conserving total energy.

Power is work done per unit time (P = W/t). It measures how fast energy is transferred.

NCERT compares a laborer lifting bricks slowly (low power) vs. a machine doing it faster (high power).

A sprinter (high power) finishes a race faster than a marathon runner (low power).

The commercial unit is kilowatt-hour (kWh), used for billing. 1 kWh = 3.6 × 10⁶ J.

NCERT states a 100W bulb running for 10 hours consumes 1 kWh, costing as per local rates.

Our electricity bill depends on total kWh consumed by appliances like fans and refrigerators.

In science, work is done when a force causes displacement. It is calculated as Work (W) = Force (F) × Displacement (s) × cosθ.

Our textbook shows lifting a book vertically, where θ=0° and cosθ=1. If force is 10N and displacement is 2m, work done is 20J.

Pushing a stalled car horizontally applies force, but if it doesn’t move, no work is done as displacement is zero.

Kinetic energy is due to motion, while potential energy is stored due to position or state.

NCERT explains a moving car has kinetic energy, whereas water stored in a dam has gravitational potential energy.

A stretched rubber band has elastic potential energy, which converts to kinetic energy when released.

Energy cannot be created or destroyed, only transformed. Total energy remains constant.

NCERT shows a swinging pendulum where potential energy converts to kinetic energy and vice versa, but total energy stays the same.

In a hydroelectric plant, water’s potential energy converts to kinetic, then to electrical energy, conserving total energy.

Power is the rate of doing work, calculated as Power (P) = Work (W) / Time (t).

NCERT compares two laborers lifting bricks: one taking 10s (higher power) and another taking 20s (lower power) for the same work.

A faster electric motor pumps water quicker, demonstrating higher power than a slower one.

Mechanical energy is the sum of kinetic and potential energy in a system.

NCERT describes a roller coaster: at the top, it has maximum potential energy, which converts to kinetic energy as it descends.

A bouncing ball loses some mechanical energy as heat/sound but mostly converts between kinetic and potential energy.

In Science, work is defined as the product of the force applied on an object and the displacement caused by that force in the direction of the force. Mathematically, it is expressed as:
Work (W) = Force (F) × Displacement (s) × cosθ, where θ is the angle between the force and displacement.

The SI unit of work is the joule (J), which is equivalent to 1 newton-meter (N·m).

Example of work done: When you push a box horizontally across the floor, and it moves in the direction of the force, work is done because both force and displacement are in the same direction (θ = 0°, cos0° = 1).

Example of work not done: If you hold a heavy bag stationary for some time, no work is done on the bag even though you apply a force because there is zero displacement (s = 0). Similarly, if you push a wall and it doesn’t move, no work is done despite applying force.

Potential Energy (PE) is the energy stored in an object due to its position or configuration. It depends on factors like height or elasticity.
Example: A book placed on a shelf has gravitational potential energy due to its height above the ground.

Kinetic Energy (KE) is the energy possessed by an object due to its motion. It depends on the mass and velocity of the object.
Example: A moving car has kinetic energy because of its motion.

Conversion of Energy: Potential energy can be converted into kinetic energy and vice versa.
Real-life scenario: When a roller coaster is at the top of a hill, it has maximum potential energy. As it descends, this energy is converted into kinetic energy, increasing its speed. At the bottom, most of the energy is kinetic, and as it climbs again, kinetic energy is converted back to potential energy.

This interconversion demonstrates the Law of Conservation of Energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

In science, work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, it is expressed as:

Work (W) = Force (F) × Displacement (s) × cosθ

where θ is the angle between the force and displacement vectors.

For work to be done, the following conditions must be met:

• A force must be applied to the object.
• The object must undergo displacement due to the applied force.
• The displacement must have a component in the direction of the force (i.e., θ ≠ 90°).

Example: Pushing a box across the floor. Here, the applied force causes the box to move (displacement), and since the force and displacement are in the same direction (θ = 0°), work is done.

Note: If you push a wall and it doesn’t move, no work is done because there is no displacement (s = 0). Similarly, holding a heavy bag stationary does no work as there is no displacement.

In scientific terms, work is said to be done when a force applied on an object causes a displacement in the direction of the force. The two essential conditions for work to be done are:

1. A force must act on the object.
2. The object must undergo displacement in the direction of the force.

Mathematically, work (W) is calculated as:

W = F × d × cosθ

where F is the force applied, d is the displacement, and θ is the angle between the force and displacement.

Example where no work is done: If a person holds a heavy bag stationary for some time, no work is done because although a force is applied (to counteract gravity), there is no displacement in the direction of the force. Hence, W = 0.

In scientific terms, work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, it is expressed as:

Work (W) = Force (F) × Displacement (s) × cosθ, where θ is the angle between the force and displacement vectors.

The relationship between work and energy is that work done on an object results in a change in its energy. For example, when work is done to lift an object, its potential energy increases. Similarly, when work is done to accelerate an object, its kinetic energy increases.

Example where work is done: Pushing a box across the floor. Here, force is applied in the direction of displacement, so work is done.

Example where no work is done: Holding a heavy bag stationary. Although force is applied, there is no displacement, so no work is done (since s = 0).

This concept is crucial in understanding how energy is transferred and transformed in real-world scenarios, aligning with the law of conservation of energy.

In physics, work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, work (W) is given by:

W = F × s × cosθ

where F is the force applied, s is the displacement, and θ is the angle between the force and the direction of displacement.

Example of work done: When you push a box horizontally across the floor, and the box moves in the direction of the applied force, work is done. Here, θ = 0°, so cosθ = 1, and W = F × s.

Example of work not done: If you hold a heavy bag stationary for some time, no work is done because there is no displacement (s = 0). Similarly, if you push a wall and it doesn’t move, no work is done.

Derivation of work done at an angle:

1. Consider a force F acting at an angle θ to the displacement s.
2. The component of force in the direction of displacement is Fcosθ.
3. Work done is the product of this component and displacement: W = (Fcosθ) × s.
4. Thus, W = F × s × cosθ.

This formula shows that work is maximum when θ = 0° (force and displacement are in the same direction) and zero when θ = 90° (force is perpendicular to displacement).

In Science, work is defined as the product of the force applied on an object and the displacement caused by that force in the direction of the force. Mathematically, it is expressed as:

Work (W) = Force (F) × Displacement (s) × cosθ, where θ is the angle between the force and displacement vectors.

The relationship between work and energy is fundamental. Work is a way to transfer energy from one system to another. When work is done on an object, its energy changes. For example, if you lift a book from the ground to a table, you do work against gravity, and the book gains gravitational potential energy.

Example: Consider pushing a stationary bicycle to make it move. Here:

1. You apply a force on the bicycle.
2. The bicycle moves in the direction of the force (displacement).
3. The work done by you transfers energy to the bicycle, increasing its kinetic energy.

Thus, work and energy are interconnected—work done results in an energy change, and energy enables the capacity to do work.

In physics, work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, it is expressed as W = F × s × cosθ, where W is work, F is the applied force, s is the displacement, and θ is the angle between the force and displacement vectors.

Work and energy are closely related. When work is done on an object, energy is transferred to or from it. For example, lifting a box against gravity increases its potential energy, while pushing a moving object increases its kinetic energy.

Example where work is done: Pushing a box horizontally across the floor. Here, the force and displacement are in the same direction (θ = 0°), so cosθ = 1, and work is done (W = F × s).

Example where no work is done: Holding a heavy bag stationary. Although force is applied, there is no displacement (s = 0), so W = 0. Similarly, if the force is perpendicular to displacement (θ = 90°), cosθ = 0, and no work is done.

The law of conservation of energy states that energy can neither be created nor destroyed, but it can only be transformed from one form to another. The total energy of an isolated system remains constant.

Example: A swinging pendulum demonstrates this law perfectly. At the highest point of its swing, the pendulum has maximum potential energy (due to height) and zero kinetic energy (as velocity is zero). As it swings down:
- Potential energy converts to kinetic energy.
- At the lowest point, kinetic energy is maximum and potential energy is minimum.
- The cycle repeats, showing continuous energy transformation without loss (assuming no friction).

Energy Transformations:

• Potential Energy → Kinetic Energy → Potential Energy (and so on).
• Total mechanical energy (PE + KE) remains constant if dissipative forces like air resistance are ignored.

The law of conservation of energy states that energy can neither be created nor destroyed, but it can only be transformed from one form to another. The total energy of an isolated system remains constant.

Example: When a ball is dropped from a height, its potential energy (due to height) converts into kinetic energy (due to motion) as it falls. At any point during the fall, the sum of potential and kinetic energy remains constant, ignoring air resistance.

Application in a simple pendulum:

• At the highest point of its swing, the pendulum has maximum potential energy and zero kinetic energy (since it momentarily stops).
• As it swings down, potential energy converts to kinetic energy.
• At the lowest point, it has maximum kinetic energy and minimum potential energy.
• The total mechanical energy (sum of kinetic and potential energy) remains constant if we ignore air resistance and friction.