Work, Energy, and Power - Comprehensive NEET Physics Notes

1. Introduction

The terms "work," "energy," and "power" are frequently used in everyday language. In physics, these terms have precise definitions and interrelations, which are crucial for understanding various physical phenomena.

2. Notions of Work and Kinetic Energy: The Work-Energy Theorem

2.1 The Scalar Product

The scalar product (or dot product) of two vectors $A$ and $B$ , denoted by $A \cdot B$ , is defined as:

$A \cdot B = A B cos θ$

where $θ$ is the angle between the vectors. The scalar product gives a scalar quantity from two vectors and follows the commutative and distributive laws.

2.2 Work

Work is defined as the product of the component of the force in the direction of the displacement and the magnitude of this displacement:

$W = F \cdot d = F d cos θ$

If there is no displacement, there is no work done even if the force is large.

Did You Know?

The SI unit of work is the joule (J), named after James Prescott Joule.

2.3 Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. For an object of mass $m$ moving with velocity $v$ , the kinetic energy (K) is given by:

$K = \frac{1}{2} m v^{2}$

Kinetic energy is a scalar quantity.

NEET Tip:

Remember that kinetic energy is always positive, as it depends on the square of the velocity.

2.4 The Work-Energy Theorem

The work-energy theorem states that the work done by the net force on an object is equal to the change in its kinetic energy:

$W = Δ K = K_{f} - K_{i}$

where $K_{f} an d K_{i}$ are the final and initial kinetic energies, respectively.

Mnemonic:

Work-Energy Theorem: "Work leads to Kinetic changes" (W = K).

Interactive Stimulation for Energy:

2.5 Example Problem

A cyclist comes to a skidding stop in 10 m. The force on the cycle due to the road is 200 N and is directly opposed to the motion. Calculate the work done by the road on the cycle.

Solution:

Work done by the road: $W = F d cos θ = 200 \times 10 \times cos 18 0^{\circ} = - 2000 J$

3. Work Done by a Variable Force

3.1 Work Done by a Variable Force

For a varying force $F (x)$ in one dimension, the work done is:

$W = \int_{x_{i}}^{x_{f}} F (x) d x$

Real-life Application:

When pushing a car, the force required varies as the car accelerates or decelerates.

4. Potential Energy

4.1 Concept of Potential Energy

Potential energy (U) is the stored energy of an object due to its position or configuration. The gravitational potential energy of an object of mass $m$ at height $h$ is:

$U = m g h$

4.2 The Conservation of Mechanical Energy

The total mechanical energy (sum of kinetic and potential energies) of a system remains constant if only conservative forces act on the system:

$E_{total} = K + U = constant$

Common Misconception:

Potential energy is not always related to height. For example, the potential energy in a spring depends on its compression or extension.

NEET Problem-Solving Strategy:

Use energy conservation to solve problems involving conservative forces. Identify the initial and final energies and set them equal to solve for unknowns.

5. Power

5.1 Power

Power (P) is the rate at which work is done or energy is transferred. It is given by:

$P = \frac{W}{t}$

The SI unit of power is the watt (W), where:

$1 W = 1 J/s$

NEET Exam Strategy:

For problems involving power, calculate work done and then divide by the time taken. Ensure units are consistent.

6. Collisions

6.1 Elastic and Inelastic Collisions

In elastic collisions, both kinetic energy and momentum are conserved. In inelastic collisions, only momentum is conserved.

6.2 One-Dimensional Collisions

For a one-dimensional elastic collision between two masses $m_{1}$ and $m_{2}$ :

$v_{1 f} = \frac{( m _{1} - m _{2} ) v _{1 i} + 2 m _{2} v _{2 i}}{m _{1} + m _{2}} v_{2 f} = \frac{( m _{2} - m _{1} ) v _{2 i} + 2 m _{1} v _{1 i}}{m _{1} + m _{2}}$

Concept Connection:

Collisions in physics often relate to chemical reactions in chemistry, where reactant particles collide to form products.

Quick Recap

Work: $W = F \cdot d$
Kinetic Energy: $K = \frac{1}{2} m v^{2}$
Work-Energy Theorem: $W = Δ K$
Potential Energy: $U = m g h$
Power: $P = \frac{W}{t}$
Conservation of Mechanical Energy: $E_{<}$