**CONTENT LIST**

**Work**

In physics, work is defined as the product of the force applied to an object and the distance over which that force is applied in the direction of the force. Mathematically, work (W) is calculated using the following formula:

W = F * d * cos(θ)

Where:

W represents work (measured in joules, J),

F is the magnitude of the force applied (measured in newtons, N),

d is the distance over which the force is applied (measured in meters, m), and

θ is the angle between the direction of the force and the direction of motion (measured in radians).

In simpler terms, work is done when a force is used to move an object over a certain distance in the direction of the force. The angle θ accounts for cases where the force is not applied in the exact direction of motion; if the force and motion are in the same direction, θ is 0 degrees, and if they are perpendicular, θ is 90 degrees, resulting in no work being done in the latter case.

Work can be positive, negative, or zero, depending on the direction of the force and the direction of motion. If the force and motion are in the same direction, work is positive (indicating energy is being added to the system). If they are in opposite directions, work is negative (indicating energy is being taken away from the system). If there is no motion or the force is applied perpendicular to the direction of motion, the work is zero.

**Work done by a variable force**

When dealing with a variable force, you can calculate the work done by integrating the force function over the distance over which the force acts. This involves breaking the path of motion into small segments, calculating the work done on each segment, and then summing up these infinitesimal contributions to find the total work done.

The formula for calculating the work done by a variable force F(x) over a certain distance is given by:

W = ∫[a, b] F(x) dx

Where:

W represents the total work done (measured in joules, J),

F(x) is the force as a function of position (measured in newtons, N), dx is an infinitesimal displacement along the path of motion,

[a, b] represents the interval or range over which the force is applied.

In this equation, you integrate the force function F(x) with respect to x over the interval[a, b], where a and b are the initial and final positions of the object being acted upon by the force. This integration sums up the work done by the force as it varies with positionalong the path.

It's important to note that the integration process can become more complex for non-constant forces, especially if the force function varies significantly with position. In such cases, you may need to use calculus techniques to evaluate the integral.

**Energy**

The energy of a body is defined as its capacity for doing work.

(1) It is a scalar quantity.

(2) Dimensions: [ML² T¯²].

It is same as that of work or torque.

(3) Units: Joule [S.I.], erg [C.G.S.]

Practical units: electron volt (eV), kilowatt hour (kWh), calories (cal)

Relation between Different Units:

1 joule = 107 erg, 1 eV = 1.6 × 10–19 joule1 kWh = 3.6 × 106 joule, 1 calorie = 4.18 joule

**Kinetic energy**

Kinetic energy is a fundamental concept in physics that describes the energy possessed by an object due to its motion. It is one of the two main forms of mechanical energy, the other being potential energy. Kinetic energy depends on both the mass and the velocity of the object and is calculated using the following formula:

KE =1/2*mv²

Where:

KE represents kinetic energy (measured in joules, J),

m is the mass of the object (measured in kilograms, kg),

v is the velocity (speed) of the object (measured in meters per second, m/s).

**Potential energy**

Potential energy is a fundamental concept in physics that represents the energy stored in an object due to its position or condition. It is one of the two main forms of mechanical energy, with the other being kinetic energy. Potential energy can take different forms depending on the specific situation but is always associated with the potential to do work.

Here are some common types of potential energy:

Gravitational Potential Energy (GPE): This type of potential energy is associated with an object's position in a gravitational field. It depends on the object's mass (m), the height (h) above a reference point, and the strength of the gravitational field (usually represented by the acceleration due to gravity, g). The formula for gravitational potential energy is:

GPE=mgh

Where:

GPE represents gravitational potential energy (measured in joules, J).

m is the mass of the object (measured in kilograms, kg).

h is the height above the reference point (measured in meters, m).

g is the acceleration due to gravity (approximately 9.81 m/s² on the surface of Earth).

Elastic Potential Energy: This type of potential energy is associated with the deformation or compression of elastic objects, such as springs or rubber bands. It depends on the spring constant (k) and the amount of deformation (x). The formula for elastic potential energy is:

Elastic Potential Energy= -1/2* kx²

Where:

Elastic Potential Energy represents the energy stored in the elastic object (measured in joules, J).

k is the spring constant (measured in newtons per meter, N/m).

x is the amount of deformation or compression (measured in meters, m).

**Work-Energy Theorem:**

The work-energy theorem is a fundamental principle in physics that relates the work done on an object to the change in its kinetic energy.It states that the work done by force acting on a body is equal to the change produced in the kinetic energy of the object.

Net Work (W)=Change in Kinetic Energy (ΔKE)𝑊 =1/2*𝑚𝑣² −1/2*𝑚𝑢²

Where:

W is the net work done on the object.

ΔKE is the change in kinetic energy of the object.

**Conservative & Non conservative force**

In physics, forces can be categorized as conservative or nonconservative based on their fundamental properties and effects on a system. These distinctions are essential in understanding the dynamics of physical systems. Let's explore both types of forces:

**Conservative Forces:**

Conservative forces are those forces that satisfy two fundamental properties:

a. Path Independence: The work done by a conservative force while moving an object from one point to another is independent of the path taken. In other words, the work done depends only on the initial and final positions of the object.

b. Work is Stored as Potential Energy: The work done by a conservative force is stored as potential energy within the system. As an object moves against a conservative force, its potential energy increases, and when it moves with the force, the potential energy decreases.

Common examples of conservative forces include:

Gravitational Force: The force of gravity is a conservative force. When an object is lifted against gravity, work is done on it, and potential energy is stored in the object-Earth system.

Elastic (Spring) Force: The force exerted by a compressed or stretched spring is conservative. Work done to compress or extend a spring is stored as elastic potential energy.

Electric and Magnetic Forces (under certain conditions): In electrostatics and magnetostatics (when magnetic fields are not changing with time), electric and magnetic forces are conservative.

**Nonconservative Forces:**

Nonconservative forces do not satisfy the properties of path independence and work-to-potential-energy conversion.

a. Path Dependence: The work done by nonconservative forces depends on the path taken by the object. Different paths can result in different amounts of work done.

b. Work is Not Stored as Potential Energy: Nonconservative forces do work on an object, but this work is not stored as potential energy. Instead, it is typically converted into other forms, such as kinetic energy or heat.

Common examples of nonconservative forces include:

Friction: Frictional forces, such as kinetic friction between surfaces, are nonconservative. The work done by friction is converted into heat, and it depends on the path of motion.

Air Resistance: The drag force experienced by an object moving through a fluid, like air or water, is nonconservative. It also depends on the object's speed and path.

Tension in a Moving Rope: The tension force in a rope or cable can be nonconservative if the rope is being moved in a way that stretches or compresses it.

**Power**

Power is a fundamental concept in physics and engineering that measures the rate at which work is done or the rate at which energy is transferred or transformed. It is a measure of how quickly a physical process occurs. The standard unit of power in the International System of Units (SI) is the watt (W), which is defined as one joule per second (1 J/s).

The formula to calculate power depends on the context and what you are trying to find. There are several different ways to express power:

Mechanical Power: In the context of mechanical work, power is the rate at which work is done. The formula for mechanical power is:

P (power) = W (work) / t (time)

Where:

P is power in watts (W).

W is work in joules (J).

t is time in seconds (s).

Electrical Power: In electrical systems, power is the rate at which electrical energy is transferred or used. The formula for electrical power is:

P (power) = V (voltage) * I (current)

Where:

P is power in watts (W).

V is voltage in volts (V).

I is current in amperes (A).

Thermal Power: In the context of heating or cooling systems, power represents the rate at which heat energy is transferred. The formula for thermal power is:

P (power) = Q (heat energy) / t (time)

Where:

P is power in watts (W).

Q is heat energy in joules (J).

t is time in seconds (s).

Luminous Power: In optics and lighting, luminous power represents the rate at which visible light is emitted or received. The unit for luminous power is the lumen (lm).

P (luminous power) = Φ (luminous flux) / t (time)

Where:

P is luminous power in lumens (lm).

Φ is luminous flux in lumens (lm).

t is time in seconds (s).

In summary, power is a measure of how quickly energy is used, transferred, or transformed in various physical processes. It is an essential concept in physics and engineering, and it helps quantify the efficiency and performance of systems and devices in a wide range of applications.