# Work

### Introduction to Work

• In physics, work is defined as the product of the force (F) applied to an object and the displacement (d) the object experiences in the direction of the force.

• The SI unit of work is the Joule (J), equivalent to a Newton-metre (Nm).

• Work is a scalar quantity, implying it has magnitude but no direction.

### Mathematical Representation of Work

• The mathematical formula for work is W = F.d.cos(θ), where W is the work done, F is the force, d is the displacement, and θ is the angle between the force and the displacement vectors.

• If the force and displacement are in the same direction (θ = 0), the formula simplifies to W = F.d.

### Work-Energy Theorem

• The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Mathematically, W = ΔKE, where ΔKE is the change in kinetic energy.

• The theorem provides a conceptual link between work and energy, as it implies work done is a form of energy transfer.

### Work Done against Gravity

• When an object of mass (m) is lifted in the direction opposite to gravity at a height (h), the work done is the product of the object’s weight (mg) and the height. Mathematically, W = m.g.h.

• Note that gravitational potential energy equals the work done against gravity to move an object from one position to another.

### Work Done by a Varying Force

• For a varying force, work done can be calculated by the integral of the force over the displacement.

• This means summing a series of infinitesimally small bits of work done by the force over tiny amounts of displacement.

### Tips for Calculating Work

• Always consider the direction of the force and the displacement in work calculations. Only the component of the force in the direction of the displacement does work.

• Remember to consider whether the force is constant or varying - this impacts the methods required for calculation.

• Develop strong knowledge and understanding of trigonometric principles - they frequently play a significant role in working out θ for calculating work done.

Mastering the concept of work and how to correctly compute it is fundamental for anyone seeking to excel in the field of mechanics. This topic is related to other essential concepts such as energy, power, and force, providing a robust foundation in physical understanding.