- Dr.Sanjaykumar Pawar
 |
| Work-Energy Theorem showing how work done by a force changes the kinetic energy of an object. |
Work-Energy Theorem Notes for NEET |
Kinetic Energy Made Easy
NOTIONS OF WORK AND KINETIC ENERGY
│
├── 1. Kinematics Relation
│ │
│ ├── Equation
│ │ └── v² − u² = 2as
│ │
│ ├── u = Initial Velocity
│ ├── v = Final Velocity
│ ├── a = Acceleration
│ └── s = Displacement
│
├── 2. Multiply by m/2
│ │
│ ├── (m/2)(v² − u²) = (m/2)(2as)
│ │
│ ├── ½mv² − ½mu² = mas
│ │
│ ├── Newton's Second Law
│ │ └── F = ma
│ │
│ └── Therefore
│ └── ½mv² − ½mu² = Fs
│
├── 3. Three-Dimensional Form
│ │
│ ├── v² − u² = 2(a·d)
│ │
│ ├── a = Acceleration Vector
│ ├── d = Displacement Vector
│ └── a·d = Dot Product
│
├── 4. Kinetic Energy (K)
│ │
│ ├── Formula
│ │ └── K = ½mv²
│ │
│ ├── Definition
│ │ └── Energy due to motion
│ │
│ ├── Unit
│ │ └── Joule (J)
│ │
│ └── Properties
│ ├── Always Positive
│ ├── Depends on Mass
│ └── Depends on Velocity²
│
├── 5. Work Done (W)
│ │
│ ├── Formula
│ │ └── W = F·d
│ │
│ ├── General Formula
│ │ └── W = Fd cosθ
│ │
│ ├── Definition
│ │ └── Force × Displacement
│ │
│ └── Unit
│ └── Joule (J)
│
├── 6. Work-Energy Equation
│ │
│ ├── Initial Kinetic Energy
│ │ └── Ki = ½mu²
│ │
│ ├── Final Kinetic Energy
│ │ └── Kf = ½mv²
│ │
│ └── Relation
│ └── Kf − Ki = W
│
├── 7. Work-Energy Theorem
│ │
│ ├── Statement
│ │ └── Change in Kinetic Energy
│ │ = Net Work Done
│ │
│ ├── Formula
│ │ └── Wnet = ΔK
│ │
│ └── Alternative Form
│ └── Wnet = Kf − Ki
│
├── 8. Types of Work
│ │
│ ├── Positive Work
│ │ ├── W > 0
│ │ ├── Force along Motion
│ │ └── Kinetic Energy Increases
│ │
│ ├── Negative Work
│ │ ├── W < 0
│ │ ├── Force opposite Motion
│ │ └── Kinetic Energy Decreases
│ │
│ └── Zero Work
│ ├── W = 0
│ ├── Force ⟂ Displacement
│ └── Kinetic Energy Constant
│
└── 9. NEET Formula Box
│
├── K = ½mv²
├── W = Fd cosθ
├── W = F·d
├── Wnet = ΔK
└── Wnet = Kf − Ki
FINAL CONCEPT
│
└── Net Work Done on a Body
└── Produces Equal Change in Kinetic Energy
└── Wnet = ΔK
CBSE Class 11 Physics
Work, Energy and Power
Topic: Notions of Work and Kinetic Energy – Work-Energy Theorem
A. Multiple Choice Questions (MCQs)
1. The kinetic energy of a body is given by:
(a) mv² (b) ½mv² (c) mv (d) m²v
Answer: (b) ½mv²
2. SI unit of work is:
(a) Newton (b) Watt (c) Joule (d) Pascal
Answer: (c) Joule
3. Work done is maximum when angle between force and displacement is:
(a) 0° (b) 45° (c) 90° (d) 180°
Answer: (a) 0°
4. If force is perpendicular to displacement, work done is:
(a) Positive (b) Negative (c) Zero (d) Infinite
Answer: (c) Zero
5. Work-Energy theorem states:
(a) Work done equals momentum (b) Work done equals force (c) Work done equals change in kinetic energy (d) Work done equals acceleration
Answer: (c)
6. Kinetic energy depends on:
(a) Mass only (b) Velocity only (c) Mass and velocity (d) Density
Answer: (c)
7. If velocity becomes twice, kinetic energy becomes:
(a) Two times (b) Four times (c) Six times (d) Eight times
Answer: (b)
8. The dimension of work and energy is:
(a) MLT⁻¹ (b) ML²T⁻² (c) ML²T⁻¹ (d) MLT⁻²
Answer: (b)
9. Negative work is done when:
(a) Force and displacement are same (b) Force is perpendicular (c) Force opposes displacement (d) Force is zero
Answer: (c)
10. The unit of kinetic energy is:
(a) Newton (b) Joule (c) Watt (d) kg
Answer: (b)
B. Very Short Answer Questions (1 Mark)
Q1. Define kinetic energy.
Answer: Kinetic energy is the energy possessed by a body due to its motion.
Q2. Write the formula of kinetic energy.
Answer: K = ½mv²
Q3. State SI unit of work.
Answer: Joule (J)
Q4. What is the work done when force is perpendicular to displacement?
Answer: Zero.
Q5. State Work-Energy theorem.
Answer: Change in kinetic energy equals the net work done on a body.
C. Short Answer Questions (2–3 Marks)
Q1. Define work done. Write its mathematical expression.
Answer:
Work done is the product of force and displacement in the direction of force.
W = Fd cosθ
where θ is the angle between force and displacement.
Q2. Why is kinetic energy always positive?
Answer:
K = ½mv²
Since mass is positive and square of velocity is always positive, kinetic energy is always positive.
Q3. Distinguish between positive and negative work.
| Positive Work | Negative Work |
|---|---|
| Force acts along displacement | Force acts opposite displacement |
| Energy increases | Energy decreases |
| Example: Pulling a cart | Example: Braking a bicycle |
Q4. Write any two applications of Work-Energy theorem.
Answer:
- Finding velocity without using time.
- Calculating work done by forces.
D. Long Answer Questions (5 Marks)
Q1. Derive Work-Energy theorem.
Answer:
From equation of motion:
v² − u² = 2as
Multiplying both sides by m/2,
½m(v² − u²) = mas
Since,
F = ma
Therefore,
½mv² − ½mu² = Fs
Now,
Kf = ½mv²
Ki = ½mu²
Thus,
Kf − Ki = W
Hence,
W = ΔK
This proves that net work done on a particle equals change in its kinetic energy.
Q2. Explain positive, negative and zero work with examples.
Answer:
-
Positive Work:
- Force and displacement in same direction.
- Example: Pulling a trolley.
-
Negative Work:
- Force opposite displacement.
- Example: Brakes on bicycle.
-
Zero Work:
- Force perpendicular to displacement.
- Example: Centripetal force in circular motion.
E. Assertion and Reason Questions
Q1.
Assertion (A): Kinetic energy is always positive.
Reason (R): Kinetic energy depends on square of velocity.
Answer: Both A and R are true and R is the correct explanation.
Q2.
Assertion (A): Work done by centripetal force is zero.
Reason (R): Centripetal force is perpendicular to displacement.
Answer: Both A and R are true and R is the correct explanation.
Q3.
Assertion (A): Negative work increases kinetic energy.
Reason (R): Negative work opposes motion.
Answer: Assertion is false but Reason is true.
Q4.
Assertion (A): SI unit of work and energy is same.
Reason (R): Both are measured in Joules.
Answer: Both A and R are true and R is the correct explanation.
F. Fill in the Blanks
- Kinetic energy of a body is ______ due to its motion.
Answer: energy
- Formula of kinetic energy is ______.
Answer: ½mv²
- SI unit of work is ______.
Answer: Joule
- Work done is zero when force is ______ to displacement.
Answer: perpendicular
- According to Work-Energy theorem,
W = ______
Answer: ΔK
G. Statement Based Questions
State whether True or False.
- Kinetic energy can be negative.
Answer: False
- Work and energy have same units.
Answer: True
- Work done is maximum when θ = 90°.
Answer: False
- Work-Energy theorem relates work and kinetic energy.
Answer: True
- Negative work decreases kinetic energy.
Answer: True
H. Match the Columns
Column A
A. Kinetic Energy
B. Work Done
C. Positive Work
D. Negative Work
E. SI Unit
Column B
-
Joule
-
½mv²
-
Force opposite displacement
-
Fd cosθ
-
Force along displacement
Answers
A → 2
B → 4
C → 5
D → 3
E → 1
I. Case Study Questions
Case Study
A student pushes a 5 kg box along a horizontal floor with a force of 20 N. The box moves 4 m in the direction of force.
Q1. What is the work done?
W = Fd
= 20 × 4
= 80 J
Answer: 80 J
Q2. If all work converts into kinetic energy, what is change in kinetic energy?
Answer: 80 J
Q3. Which theorem relates work and kinetic energy?
Answer: Work-Energy theorem.
Q4. Is the work positive or negative?
Answer: Positive.
Q5. Why?
Answer: Force and displacement are in the same direction.
J. Important Board Exam Questions
- Define kinetic energy.
- State and prove Work-Energy theorem.
- Write SI unit of work and energy.
- Differentiate positive and negative work.
- Explain zero work with example.
- Define work done and derive its expression.
- Explain Work-Energy theorem with suitable example.
- Why is kinetic energy always positive?
- Give practical applications of Work-Energy theorem.
- Derive K = ½mv² from Work-Energy theorem.
One-Line Revision
• K = ½mv²
• W = Fd cosθ
• Wnet = ΔK
• Positive Work → KE increases
• Negative Work → KE decreases
• Zero Work → KE remains constant
• SI Unit of Work & Energy = Joule (J)
• Work-Energy Theorem: Net work done = Change in kinetic energy
Internal Links
Laws of Motion Explained for NEET
Work, Energy and Power Complete Notes
Conservation of Mechanical Energy
Motion in a Straight Line Notes
Motion in a Plane and Vectors
Newton's Laws of Motion Questions
Circular Motion for NEET
Units and Dimensions Physics Notes
Kinematics Formula Sheet
NEET Physics Chapter-wise Revision Notes
NOTIONS OF WORK AND KINETIC ENERGY
THE WORK–ENERGY THEOREM
1. Equation from Kinematics
For rectilinear motion under constant acceleration:
Where:
- u = Initial velocity
- v = Final velocity
- a = Acceleration
- s = Displacement
This equation relates velocity, acceleration and displacement.
2. Multiplying by m/2
Multiply both sides by m/2:
From Newton's Second Law:
Therefore:
3. Generalisation to Three Dimensions
For motion in three dimensions, vectors are used.
Where:
- a = Acceleration vector
- d = Displacement vector
- · = Dot product
Multiplying by m/2:
Since:
We get:
4. Kinetic Energy (K)
The quantity
is called Kinetic Energy.
Definition
Kinetic Energy is the energy possessed by a body due to its motion.
SI Unit
Important Facts
- Kinetic energy is always positive.
- It depends on mass and velocity.
- If velocity doubles, kinetic energy becomes four times.
- If velocity becomes three times, kinetic energy becomes nine times.
5. Work Done (W)
The quantity
is called Work Done.
Definition
Work is said to be done when a force produces displacement in an object.
Formula
Where:
- F = Force
- d = Displacement
- θ = Angle between force and displacement
SI Unit
6. Work-Energy Equation
Initial kinetic energy:
Final kinetic energy:
Substituting in the equation:
7. Work-Energy Theorem
Statement
Mathematically:
or
8. Physical Meaning of Work-Energy Theorem
Case 1: Positive Work
Force acts in the direction of motion.
Result: Speed increases.
Example: Pushing a moving cart.
Case 2: Negative Work
Force acts opposite to the direction of motion.
Result: Speed decreases.
Example: Applying brakes on a bicycle.
Case 3: Zero Work
Force acts perpendicular to displacement.
Result: No change in speed.
Example: Centripetal force in circular motion.
9. Quick NEET Revision Box
Kinetic Energy
K = ½mv²
Work Done
W = Fd cosθ
Work-Energy Theorem
Wnet = Kf − Ki = ΔK
SI Unit
- Work → Joule (J)
- Kinetic Energy → Joule (J)
Key Idea
Net work done on a body changes its kinetic energy.
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