Understanding the Definition of Work in Physics
In physics, the term 'work' has a very specific definition that differs from its everyday usage. It's a fundamental concept in mechanics, directly related to energy transfer. To understand competitive exams like JEE, mastering this definition is crucial.
The Physics Definition of Work
In physics, work is done when a force causes a displacement. Specifically, work is the product of the magnitude of the applied force and the displacement of the object in the direction of the force. If the force is not parallel to the displacement, we consider only the component of the force that acts along the direction of motion.
Work is done when a force causes an object to move.
Work is a measure of energy transfer that occurs when a force is applied to an object, and that force causes the object to move a certain distance. Both force and displacement are essential for work to be done.
Mathematically, work (W) is defined as the dot product of the force vector (F) and the displacement vector (d): W = F ⋅ d. This can also be expressed as W = |F| |d| cos(θ), where θ is the angle between the force vector and the displacement vector. If the force is constant and in the same direction as the displacement (θ = 0°), then cos(θ) = 1, and W = Fd. If the force is perpendicular to the displacement (θ = 90°), then cos(θ) = 0, and no work is done by that force.
- A force must be applied. 2. The object must be displaced in the direction of the force (or a component of the force).
Units of Work
The standard unit of work in the International System of Units (SI) is the joule (J). One joule is defined as the work done when a force of one newton (N) moves an object through a distance of one meter (m) in the direction of the force. In the CGS system, the unit of work is the erg, where 1 erg = 1 dyne-cm.
| System | Unit of Force | Unit of Displacement | Unit of Work |
|---|---|---|---|
| SI | Newton (N) | Meter (m) | Joule (J) |
| CGS | Dyne | Centimeter (cm) | Erg |
Remember: If an object is stationary, no matter how large the force applied, no work is done if there is no displacement.
Work Done by Different Forces
It's important to consider the direction of the force relative to the displacement. If a force acts at an angle θ to the displacement, only the component of the force parallel to the displacement (F cos θ) contributes to the work done. If multiple forces act on an object, the net work done is the sum of the work done by each individual force.
Visualizing Work: Imagine pushing a box across a floor. If you push horizontally and the box moves horizontally, you are doing work. If you push downwards at an angle, only the horizontal component of your push contributes to the work done in moving the box forward. If you lift the box vertically, the work done is by the upward force against gravity.
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When the force is perpendicular to the displacement, or when there is no displacement.
Key Takeaways for JEE Preparation
For JEE Physics, focus on the scalar nature of work, its dependence on both force and displacement, and the role of the angle between them. Understanding W = Fd cos(θ) is fundamental for solving problems involving inclined forces or multiple forces acting on an object.
Learning Resources
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