Unraveling the Wonders of Work in Physics
Introduction
Physics, the fundamental science that explores the nature of the universe, encompasses a vast array of phenomena. Among its many captivating concepts, "work" stands as a central pillar. Work, in the context of physics, is not confined to just labor or effort; it refers to the transfer of energy that brings about a change in a system. In this blog, we'll delve into the intriguing world of work in physics, exploring its definition, formulae, and the profound impact it has on our understanding of the natural world.
Defining Work in Physics
If force is applied to an object causing the object to be displaced, then work is said to be done. When an object is pulled or pushed and doesn't change its position, according to physics no work is done, only when the object is displaced, then work is said to be done.
Work is directly proportional to the applied to it. i.e \( W \propto {\vec{F}} \). ......1.1
Work done is also directly proportional to displacement. i.e. \( W \propto {\vec{d}} \) .....1.2
Work is defined as the product of force and displacement. When a force acts on an object, causing it to move through a distance, work is done on that object. From equations 1.1 and 1.2, we get
\( W \propto {\vec{F}} \cdot {\vec{d}} \)\(\implies W=F\cos\theta \times d \) $$\implies \boxed{W={F}{d} \cos\theta} $$
Where \( \theta \) is angle beween Force \( \vec{F} \), Displacement \(\vec{d} \) and W = Work done
It's essential to note that work is a scalar quantity, meaning it has magnitude but no direction. However, the force and displacement involved are vector quantities and, therefore, their directions play a significant role in determining the overall work done.
Zero, Positive and Negative Work
When the displacement is at right angles to the applied force (θ = 90°), the work done is zero.
\(W={F}{d}\cos90^{\circ} \implies W={0} \)
For example, A porter walking with a load on his head, the force applied is perpendicular to the displacement. So, work done by him is equal to zero.
\(W={F}{d}\cos0^{\circ} \implies W={F}{d} \)
For example, when you push a box along the floor, the force applied (your push) and the displacement (forward motion) are in the same direction, leading to positive work.
Conversely, when the force and displacement have an angle of θ = 180° between them, the work done is negative. Negative work signifies that the force opposes the object's motion or slows it down.
\(W={F}{d}\cos180^{\circ} \implies W={-F}{d} \)
For example, when you lift a book off the ground, the force applied (gravity) and the displacement (upward motion) are in opposite directions, resulting in negative work.
Work Done by the Force of Gravity
All bodies are attracted towards the center of earth due to force of gravity. The work done by the force of gravity on an object depends on the displacement of the object and its weight (mass times the acceleration due to gravity). When an object is moved vertically in the presence of a gravitational field, gravity does work on the object.
Force due to gravity (weight) \(F={m}{g} \), where m is mass of object and g is the acceleration due to gravity (approximately 9.81 m/s² near the Earth's surface),
The formula to calculate the work done by the force of gravity is:
\( W={mg}{h}\cos0^{\circ}\)
\(\implies \boxed{W = mg h}\)
where:
\(W\) is the work done by gravity,
\(m\) is the mass of the object,
\(h\) is the vertical displacement of the object.
The work done by gravity can be positive or negative depending on the direction of displacement. If the object moves upward (against the force of gravity), the work done is negative, as gravity opposes the motion. On the other hand, if the object moves downward (in the direction of gravity), the work done is positive.
For example:
- If you lift a box of 5 kg vertically upward by 2 meters, the work done by gravity is:
\(W = {5} kg \times {9.81} m/s² \times {2} m = {98.1} Joules\) (positive work, as it moves in the direction of gravity). - If you lower the same box of 5 kg vertically downward by 2 meters, the work done by gravity is:
\(W = {5} kg \times {9.81} m/s² \times({-2} m) = {-98.1} Joules\) (negative work, as it moves against the force of gravity).
In both cases, the magnitude of the work done is the same, but the sign indicates the direction of the work.
Conservative and Non-conservative Forces
In the realm of work, forces are often categorized as either conservative or non-conservative. Conservative forces are path-independent, meaning the work done by these forces is only dependent on the initial and final positions of the object, and not the path taken. Examples of conservative forces include gravitational forces and elastic forces.
On the other hand, non-conservative forces are path-dependent, meaning the work done depends on the specific path taken by the object. Friction and air resistance are typical examples of non-conservative forces, as the work they do varies depending on the object's motion and the surfaces involved.
Units of Work
The unit of work in the International System of Units (SI) is the Joule (J). One Joule is defined as the amount of work done when a force of one Newton is applied to move an object one meter in the direction of the force.
Mathematically, one Joule can be expressed as:
\(\boxed{{1} Joule = {1} Newton \times {1} meter}\)
Since work is defined as the product of force and displacement, the Joule is equivalent to one Newton-meter (N·m). Another common unit of work is the kilojoule (kJ), which is equal to 1000 Joules.
In summary, the unit of work, whether in the SI system or its multiples, is the Joule (J), and it represents the amount of energy transferred or expended when a force is applied to move an object over a certain distance.
In the CGS (centimeter-gram-second) system of units, the unit of work is the erg. The erg is a smaller unit of energy compared to the Joule in the SI system.
One erg is equal to the work done when a force of one dyne (the CGS unit of force) is applied to move an object one centimeter in the direction of the force.
Mathematically, one erg can be expressed as:
\(\boxed{{1} erg = {1} dyne \times {1} centimeter}\)
Since work is defined as the product of force and displacement, the erg is equivalent to one dyne-centimeter (dyn·cm).
The conversion between the SI unit of work (Joule) and the CGS unit of work (erg) is as follows:
1 Joule = 10^7 ergs
Therefore, the erg is a much smaller unit of work compared to the Joule. It is still used in some scientific fields, particularly in astronomy and certain areas of physics, but the Joule is the more widely used unit in modern scientific practice.
Applications of Work in Physics
1. Mechanical Work: In everyday life, work is often associated with mechanical processes, such as pushing a car or lifting objects. Understanding work in physics enables us to calculate the amount of energy required for such tasks, helping engineers design efficient machines and structures.
2. Conservation of Energy: Work plays a crucial role in the law of conservation of energy, which states that energy cannot be created nor destroyed; it can only change form. Through the concept of work, physicists can trace the transformation of energy from one form to another in various systems.
3. Thermodynamics: Work is an essential concept in thermodynamics, where it is used to describe the exchange of energy in heat engines and other thermodynamic processes.
Conclusion
In conclusion, work in physics is an intriguing and fundamental concept that reveals the intricate relationship between force, displacement, and energy transfer. From its mathematical representation to its real-world applications, work forms a cornerstone in our understanding of the natural world and is pivotal in fields ranging from mechanics to thermodynamics. As we continue to delve deeper into the realm of physics, we unlock new possibilities and enrich our comprehension of the universe's inner workings.