Work is an important concept in physics that we use in daily life. But in science, work has a special meaning. It is done when a force is applied to an object, and the object moves in the direction of the force. For example, lifting a book, pushing a door, or pulling a cart are all examples of work.
In this article, we will learn about the types of work in physics, their definitions, SI units, and dimensions. This topic is important for competitive exams like SSC, Banking, RRB NTPC, UPSC, and State-level exams. Understanding this concept will help you solve numerical problems and answer theoretical questions easily. Let’s get started!
Introduction
In our daily lives, we often consider activities like reading books, writing notes, listening to music, or painting as “work.” However, in physics, the definition of work is more precise. It depends on two key factors: force applied and displacement of an object. Unlike everyday usage, work in physics involves formulas, SI units, and numerical values.
Understanding the concept of work, its types, SI units, and dimensions is crucial for exams like SSC, Banking, RRB NTPC, UPSC, and State-level exams. In this guide, we will break down these concepts in a simple and easy-to-understand manner. Keep reading to boost your exam preparation!
Definition of Work
In physics, work is defined as the transfer of energy from one object to another due to a force applied, causing displacement. It is a scalar quantity and depends on the magnitude of force, displacement, and the angle (θ) between them.
Work Formula in Physics
The mathematical expression for work is: W=Fdcosθ
Where:
- W = Work done
- F = Force applied
- d = Displacement of the object
- θ = Angle between force and displacement
Work as a Dot Product
In vector form, work is the dot product of force and displacement: W=F⋅d
Or, W=(Fcosθ)d
Here, F cos θ is the component of force in the direction of displacement.
Maximum and Minimum Work Done
- Maximum Work occurs when θ = 0°, meaning force and displacement are in the same direction.
- Minimum Work (zero) occurs when θ = 90°, meaning force is perpendicular to displacement (e.g., carrying a bag while walking).
Is Work a Vector or Scalar?
Work: A Scalar or Vector Quantity?
One of the most common questions in physics is whether work is a vector or scalar quantity. Let’s clarify this concept with a proper explanation.
Is Work a Scalar Quantity?
✔️ Yes, work is a scalar quantity.
Why is Work a Scalar Quantity?
We can determine whether work is scalar or vector by analyzing its formula: W=Fdcosθ
Where:
- W = Work
- F = Force (Vector)
- d = Displacement (Vector)
- θ = Angle between force and displacement
Both force and displacement are vector quantities, but work is the dot product (scalar product) of two vectors, which always results in a scalar quantity.
Key Explanation
✅ Dot Product of Two Vectors: The formula for work involves the dot product, and the result of a dot product is always a scalar quantity, not a vector.
✅ No Direction: Unlike vectors, work does not have a specific direction; it only has magnitude.
✅ Energy Transfer: Work represents the energy transferred by an external force, which is a scalar concept.
Since work has magnitude but no direction, it is classified as a scalar quantity in physics.
Unit of Work in Physics
What is the Unit of Work?
The unit of work depends on the system of measurement used. The two most commonly used units are:
✔️ SI Unit of Work: Joule (J)
✔️ CGS Unit of Work: Erg
SI Unit of Work: Joule (J)
🔹 The SI unit of work is the joule (J), named after James Prescott Joule, a British physicist.
🔹 It is a derived unit of energy in the International System of Units (SI).
Definition of Joule (J)
💡 One joule is the work done when a force of one newton (N) moves an object by one meter (m) in the direction of the applied force.
1 Joule=1 Newton × 1 Meter (1J=1N⋅m)
Explanation
✔️ Force (F) = Newton (N)
✔️ Displacement (d) = Meter (m)
✔️ Work (W) = Force × Displacement = Newton × Meter = Joule (J)
📌 Example Calculation:
If a 1 N force moves an object 1 meter, then: W=1N×1m=1JW = 1N \times 1m = 1JW=1N×1m=1J
So, 1 joule is the work done by a force of 1 newton moving an object 1 meter.
CGS Unit of Work: Erg
🔹 In the Centimeter-Gram-Second (CGS) system, the unit of work is Erg.
🔹 1 Erg = 10−7 Joules
🔹1 Erg=1 dyne×1 cm
🔹Since 1 dyne = 10−5 newtons and 1 cm = 10−2 meters, we get:
🔹1 Erg=10−5 N×10−2m=10−7J
Key Takeaways
🔹 SI unit of work = Joule (J)
🔹 CGS unit of work = Erg
🔹 1 J = 1 N·m
🔹 1 Erg = 10−710^{-7}10−7 J
🔹 Work is the product of force and displacement
Dimensional Formula of Work and Its Derivation
The dimensional formula of work is an important concept in Work, Power, and Energy and is frequently asked in exams like SSC, RRB NTPC, and other competitive exams. Understanding the dimensional analysis of work helps in solving numerical problems and verifying physical equations.
Dimensional Formula of Work
✅ The dimensional formula of work is: [ML2T−2]
Derivation of the Dimensional Formula of Work
Work is mathematically expressed as: W=F×d
Where:
- W = Work
- F = Force
- d = Displacement
Step 1: Dimensional Formula of Force
From Newton’s Second Law of Motion: F=m×a
Where:
- m = Mass (Dimensional formula = [M])
- a = Acceleration (Dimensional formula = [LT−2] )
Thus, the dimensional formula of force is: [M][LT−2]=[MLT−2]
Step 2: Dimensional Formula of Work
Since Work = Force × Displacement, we substitute the dimensions: [MLT−2]×[L]=[ML2T−2]
Thus, the dimensional formula of work is: [ML2T−2]
📌 Key Point: The unit and dimensional formula of work and energy are the same, since energy is also measured in Joules and follows the same formula.
Alternative Units of Work and Energy
Work and Energy are measured in different units across various systems. Below are some important conversions:
| Unit | Equivalent in Joules (J) |
|---|---|
| Erg | 1 erg=10−7J |
| Electron Volt (eV) | 1eV=1.6×10−19J |
| Calorie (cal) | 1cal=4.186J |
| Kilowatt Hour (kWh) | 1kWh=3.6×106J |
Key Takeaways
✔️ Dimensional formula of work = [ML2T−2]
✔️ Work is the product of force and displacement
✔️ The unit of work and energy is the same (Joule in SI units)
✔️ Understanding dimensions helps in unit conversion and equation verification.
Different Types of Work Done in Physics
Understanding the types of work and conditions for zero work is crucial for solving tricky questions in physics, especially in topics like Work, Power, and Energy. Here, we will break down the types of work based on the angle between the force and displacement vectors.
Types of Work Done
Work can be classified into positive work, negative work, and zero work based on the angle (θ) between the direction of force and displacement.
Condition for Positive Work
🔹 When 0∘≤θ≤90∘, cos θ is positive, and the work done is also positive.
🔹 Mathematical Expression: W=F×d×cos(θ)
When θ=0∘ (i.e., force and displacement are in the same direction), cos(0) = 1, and the formula simplifies to: W=F×d
Example:
A boy pulls an object towards himself. Here, the force and displacement are in the same direction, so the work done is positive.
Condition for Negative Work
🔹 When 90∘≤θ≤180∘, cos θ is negative, which makes the work done negative.
🔹 Mathematical Expression: W=F×d×cos(θ)
When θ=180∘ (i.e., force and displacement are in opposite directions), cos(180) = -1, and the formula becomes: W=−F×d
Example:
In the case of frictional force acting on a body sliding over a rough surface, the angle between the direction of force (friction) and displacement is 180∘, so the work done by friction is negative.
Condition for Zero Work
🔹 When θ=90∘, the force is perpendicular to the direction of displacement, meaning cos(90) = 0, so the work done is zero.
🔹 Example:
If a person is carrying a heavy box horizontally while walking, the force is acting vertically upward to support the box, but the displacement is horizontal. In this case, the angle between force and displacement is 90∘, so the work done is zero.
Summary of Work Done Conditions
| Angle (θ) | Work Done | Type of Work |
|---|---|---|
| 0∘≤θ≤90∘ | Positive | Positive Work |
| 90∘<θ≤180∘ | Negative | Negative Work |
| θ=90∘ | Zero | Zero Work |
Key Takeaways
✔️ Positive Work: Force and displacement are in the same direction (θ between 0° and 90°).
✔️ Negative Work: Force and displacement are in opposite directions (θ between 90° and 180°).
✔️ Zero Work: Force is perpendicular to displacement (θ=90∘).
Conditions for Zero Work or No Work Done
In physics, zero work or no work done occurs when certain conditions are met. Understanding these conditions is important for solving problems related to Work, Power, and Energy. Here, we’ll explore the different situations where no work is done.
Conditions for Zero Work
When Displacement is Zero
If the displacement of the object is zero, no work is done on the object, even if a force is applied.
- Example 1: A weightlifter holding a 150 kg mass steadily on his shoulder for 30 seconds does no work on the load because there is no displacement of the weight during that time.
- Example 2: When we push against a rigid wall, the force we exert on the wall does not cause any displacement (i.e., d=0), so no work is done on the wall, though our muscles are still expending energy.
- Example 3: When an object moves in a circular path, the total work done after completing one full circle is zero, because the initial and final position of the object are the same, implying zero displacement.
When Force is Zero
- If no force is applied to the object, no work can be done, regardless of the displacement.
- Example: A block moving on a smooth horizontal table experiences no horizontal force (since there is no friction), even though it may undergo displacement. In this case, no work is done by any horizontal force.
When Force and Displacement are Perpendicular
If the angle between the direction of force and the direction of displacement is 90° (θ=90∘ or θ=π/2 radians), the work done is zero because cos90∘=0
- Mathematical Expression: W=F×d×cos(θ)=F×d×cos(90∘)=0
- Example 1: When a block moves on a smooth horizontal table, the gravitational force (mgmg) does no work since it acts vertically downward, and the displacement is horizontal, making the angle between force and displacement 90°.
- Example 2: A coolie carrying a load on his head while moving forward experiences the weight of the load acting vertically downward, while his displacement is horizontal. Since the force and displacement are perpendicular, no work is done on the load.
Summary of Zero Work Conditions
| Condition | Explanation |
|---|---|
| Condition 1: Zero Displacement | When the displacement of the object is zero (d=0), no work is done. |
| Condition 2: Zero Force | If no force is applied to the object, no work is done, even if the object moves. |
| Condition 3: Force and Displacement are Perpendicular | When the angle between force and displacement is 90° (θ=90∘), no work is done. |
Key Takeaways
✔️ Zero work occurs when:
- The displacement is zero,
- The force is zero,
- The force and displacement are perpendicular (90° angle).
✔️ In all these conditions, although forces might be acting on the object, no work is done because work depends on the displacement and the angle between force and displacement.
PYQs on Types of Work Done
Here, we provide all the MCQs on ‘Work’ of the topic Work Power and Energy formulas which is important for almost all competitive exams like SSC, RRB NTPC, CDS, UPSC, and all state PSCs (both prelims and mains)
1. Which of the following pairs of physical quantities have the same dimensions?
(SSC CHSL (10+2) LD 2015)
A. Force and Power
B. Work and Power
C. Work and Energy
D. Momentum and Power
2. If a body moves with a constant speed in a circle _
(SSC CHSL (10+2) DEO & LDC 2014)
A. no work is done on it
B. no force acts on it
C. no acceleration is produced in it
D. its velocity remains constant
3. One electron volt is equal to _
A. 6× 10-17 J
B. 6× 10-19 J
C. 1.6× 10-17 J
D. 6.5× 10-10 J
4. The SI unit of Work is _
A. Joule-second
B. Kwhr
C. Watt
D. Joule
5. The Work Done by the Centripetal Force for a Body Moving in a Circular Path is __?
A. Negative
B.Positive
C.Constant
D. Zero
6. The work done is Zero if _
A. The body shows displacement in the opposite direction of the force applied.
B. The body shows displacement in the same direction as the force applied.
C. The body shows a displacement in a perpendicular direction to the force applied.
D. The body masses obliquely to the direction of the force applied
7. The unit of work is joule. The other physical quantity that has the same unit is _
A. power
B. velocity
C. energy
D. force
8. When can one say that work is done on the body _
A. When the body experiences force
B. When there is an increase in energy because of mechanical influence
C. When the body moves a certain distance
D. None of the above
9. When the force retards the motion of the body, the work done is _
A. Positive
B. Negative
C. Zero
D. None of these
10. A man pushes a wall and fails to displace it, he does _
A. Maximum positive word
B. Negative work
C. Positive but not maximum work
D. No work at all
11. The work done by a Boy who is carrying a box on his head is walking on a level road _
A. Positive
B. Negative
C. Zero
D. None of these
12. A metal ball moves in a frictionless inclined table without slipping. The word done by the table surface on the ball is
A. Positive
B. Negative
C. Zero
D. None of these
13. What happens to the body on which work is done _
A. First it loses, then it gains
B. No change in the energy
C. It gains energy
D. It loses energy
14. On an object, the work done does not depend upon_
A. Initial velocity of an object
B. Displacement
C. Force applied
D. Angle between force and displacement
15. What are the dimensions of Work?
A. M L2 T-2
B. M L2 T-3
C. M L-1 T-1
D. M L-3 T-1
16. Work is a _
A. Vector Quantity
B. Tensor quantity
C. Scalar Quantity
D. None of these
17. 1 erg equal to _
A.3.6× 107 J
B.10-10 J
C. 10-7 J
D. None of these
18. Work done by the frictional force is _
A. Positive
B. Negative
C. Zero
D. None of these
19. Work done by the gravitational force on a body moving on a smooth
horizontal surface _
A. Positive
B. Negative
C. Zero
D. None of these
20. 1 newton-meter (N⋅m) is equal to _
A. 10-7 erg
B.0.2389 Cal
C. 1 Joule
D. All of the above
🔰Source – NCERT Class 11 Physics
