SI and CGS Units of Work: Differences, Conversion, and Examples
Work is a fundamental concept in Physics, especially in Mechanics. It helps us understand how forces cause changes in the state of motion and energy of objects. Whenever a force acts upon an object and causes displacement, work is said to be done. Understanding the unit of work, its calculation, and its real-world applications is essential for building a solid foundation in Physics.
Definition of Work in Physics
Work is defined as the product of force and displacement in the direction of the force. In simple terms, if you apply a force to move something, the amount of work done depends on both the strength of the force and how far the object moves. The mathematical expression for work is:
W = F × s × cos θ
Here, W stands for work, F is the magnitude of the applied force, s is the magnitude of displacement, and θ is the angle between the direction of force and displacement.
Units of Work: SI and CGS Systems
The unit of measurement for work depends on the system of units used.
| System | Unit Name | Symbol | Definition | Relation |
|---|---|---|---|---|
| SI (International System) | Joule | J | Work done by a force of 1 newton causing displacement of 1 meter in the direction of the force | 1 J = 1 N × 1 m |
| CGS (Centimetre-Gram-Second System) | Erg | erg | Work done by a force of 1 dyne causing displacement of 1 cm | 1 erg = 1 dyne × 1 cm |
Conversion between SI and CGS units is common in Physics. One joule is equivalent to 107 ergs.
| From | To | Conversion Factor |
|---|---|---|
| Joule (J) | Erg (erg) | 1 J = 107 erg |
| Erg (erg) | Joule (J) | 1 erg = 10-7 J |
Formula Derivation and Explanation
Work is calculated using the formula:
W = F × s × cos θ
If the force and displacement are in the same direction, θ = 0°, so cos θ = 1, and the formula simplifies to W = F × s. If the angle is 90°, work becomes zero. When θ is more than 90°, work is negative.
Examples: Calculating Work in Physics
Let’s see two typical examples to clarify the calculation steps:
-
Example 1: A force of 10 N moves a body by 3 meters in the direction of the force. Find the work done.
Solution:
Work = Force × Displacement = 10 N × 3 m = 30 Joules -
Example 2: How many ergs are in 5 Joules of work?
Solution:
1 Joule = 107 erg
5 Joules = 5 × 107 erg = 50,000,000 erg
Key Points while Solving Work Problems
- Always use SI units (newton for force, meter for displacement) unless stated otherwise.
- Remember to use the angle in the formula: use cos θ if force and displacement are not in the same direction.
- If there is no displacement, no work is done, even if a force is applied.
Table: Work Formula and Applications
| Scenario | Formula | Application |
|---|---|---|
| Force and displacement in same direction | W = F × s | Easiest case, θ = 0° |
| Force and displacement at angle θ | W = F × s × cos θ | Use for all cases with angle |
| Force perpendicular to displacement | W = 0 | No work done, θ = 90° |
Types of Work: Positive, Negative, and Zero
| Type | Angle (θ) | Description | Example |
|---|---|---|---|
| Positive Work | 0° < θ < 90° | Force component along displacement | Pushing a box forward |
| Negative Work | 90° < θ ≤ 180° | Force opposite to displacement | Friction stopping a moving object |
| Zero Work | θ = 90° | Force perpendicular to displacement | Carrying bag horizontally |
Step-by-Step Approach to Problem Solving
- Write down what is given: force, displacement, and angle.
- Convert all values to SI units (N, m, degree).
- Select the correct formula based on the angle between force and displacement.
- Substitute values and solve.
- Double-check unit conversions if needed.
Explore More Physics Concepts
- Work and Energy
- Work Done - Additional Examples
- Work, Energy and Power
- Derivation of Work-Energy Theorem
- Force, Work and Energy
- Difference between Work and Energy
Practice Questions
- Calculate the work done when a force of 5 N moves an object by 8 meters at an angle of 60° to the direction of force.
- Convert 2 Joules of work to ergs.
- Explain why no work is done if the force is perpendicular to the direction of displacement.
Conclusion
Work is a vital concept to understand energy transfer and motion in Physics. Practice regular problem solving, pay attention to units, and always consider the direction of force and displacement to be accurate in your calculations. For deeper learning and more topics, explore the linked Vedantu Physics resources.
FAQs on Understanding Unit of Work in Physics: Definition, Units, and Formulas
1. What is the SI unit of work?
The SI unit of work is the Joule (J). Work is defined as the product of force and displacement in the direction of force.
- 1 Joule is the work done when a force of 1 newton moves an object 1 meter in the direction of the force.
- Formula: Work (W) = Force (F) × Displacement (s)
- SI units: Force in newtons (N), displacement in meters (m)
2. What is the CGS unit of work?
The CGS unit of work is the Erg.
- 1 Erg is the work done when a force of 1 dyne moves an object 1 centimeter in its direction.
- Formula: Work (W) = Force (F) × Displacement (s) (in CGS: F in dyne, s in cm)
- 1 Joule (J) = 107 ergs
3. How do you convert joule to erg?
To convert joule to erg, multiply the value in joules by 107.
- 1 Joule = 107 ergs
- Example: 2 Joule = 2 × 107 = 20,000,000 ergs
4. Write the formula for work in physics.
The formula for work is:
- W = F × s × cos θ
- Where W = Work, F = Force applied, s = Displacement, θ = Angle between force and displacement
- If force and displacement are in the same direction, θ = 0, so cos 0 = 1, thus W = F × s
5. What is meant by 1 Joule of work?
1 Joule of work is done when a force of 1 newton moves a body by 1 meter in the direction of the force.
- 1 Joule = 1 Newton × 1 Meter
- It is the standard measurement unit for work in the SI system.
6. Is erg a unit of work? How does it differ from joule?
Yes, erg is a unit of work in the CGS system.
- 1 erg = work done by 1 dyne force moving an object 1 cm
- SI Unit (Joule): Used globally in science and engineering—1 joule = 107 ergs
- Joule is a larger unit compared to erg
7. What is the dimensional formula of work?
The dimensional formula of work is [M1 L2 T-2].
- Derived from: Work = Force × Displacement
- Force: [M1 L1 T-2], Displacement: [L1]
- Therefore, [M1 L2 T-2]
8. Why is no work done if the displacement is perpendicular to the force?
No work is done when displacement is perpendicular to the applied force because the angle θ = 90°.
- W = F × s × cos θ
- cos 90° = 0, so W = 0
- This means the force does not contribute to movement in its direction.
9. Give two real-life examples of work being done in physics.
Examples of work done in physics:
- Lifting a book vertically upwards (force and displacement in same direction)
- Pushing a cart along the floor (applying force, moving it in that direction)
- Both satisfy: Work = force × displacement in direction of force
10. What is negative work? Provide an example.
Negative work occurs when force and displacement are in opposite directions (θ = 180°).
- Example: When brakes are applied to a moving bike, friction acts in the direction opposite to motion, resulting in negative work.
- Here, W = F × s × cos 180° = -F × s
11. State the difference between work, energy, and power.
Work, energy, and power are related but distinct physical quantities:
- Work: Transfer of energy by applying force over a displacement (unit: joule)
- Energy: The capacity to do work (unit: joule)
- Power: Rate at which work is done or energy is transferred (unit: watt)
12. How do you ensure your answer has the correct unit in physics problems involving work?
To ensure correct units in work calculations:
- Always use SI units: force in newtons (N), displacement in meters (m)
- Convert CGS units (dyne, cm) to SI if needed
- Final answer should be expressed in joules (J) unless otherwise specified
