HC VERMA | CHAP-8 | WORK AND ENERGY - EXERISE-Q11-Q20 | IIT JEE | NEET

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Work and energy are fundamental concepts in physics that are deeply interconnected.

*Work:* In physics, work is done when a force acts upon an object to cause a displacement in the direction of the force applied. Mathematically, work (W) is defined as the product of the force (F) applied to an object and the distance (d) over which the force acts, where the force and the displacement are in the same direction. The formula for work is:

\[ W = F \cdot d \cdot \cos(\theta) \]

Where:
\(W\) = Work done
\(F\) = Applied force
\(d\) = Displacement
\(\theta\) = Angle between the force and the direction of displacement

Work can be positive, negative, or zero. If the force and the displacement are in the same direction, work is positive. If they're in opposite directions, work is negative. If the force is perpendicular to the displacement, work is zero.

*Energy:* Energy is the ability to do work. It exists in various forms such as kinetic energy, potential energy, thermal energy, chemical energy, and more. The two primary forms of energy relevant to work are:

*Kinetic Energy:* The energy possessed by an object due to its motion. It's directly related to the object's mass and its velocity and is given by the formula:

\[ KE = \frac{1}{2} \cdot m \cdot v^2 \]

Where:
\(KE\) = Kinetic energy
\(m\) = Mass of the object
\(v\) = Velocity of the object

*Potential Energy:* The energy stored in an object due to its position or state. For example, gravitational potential energy is related to an object's position concerning the Earth's surface and is given by:

\[ PE = m \cdot g \cdot h \]

Where:
\(PE\) = Potential energy
\(m\) = Mass of the object
\(g\) = Acceleration due to gravity
\(h\) = Height of the object

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another.

The relationship between work and energy is described by the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. This theorem is expressed as:

\[ W = \Delta KE \]

This means that the work done on an object causes a change in its kinetic energy. If positive work is done on an object, its kinetic energy increases, while negative work decreases the kinetic energy.

Understanding work and energy is crucial in various fields, including mechanics, thermodynamics, and fields related to energy transformation and conservation.