- Dr.Sanjaykumar Pawar
 |
Kinetic Energy and Work Done by Variable Force explained with formulas, examples, and graphical interpretation for NEET aspirants. |
INTERNAL LINK SUGGESTIONS
Laws of Motion Complete Notes
Motion in One Dimension Notes
Motion in a Plane Notes
Work Energy Theorem Explained
Potential Energy Notes
Conservation of Energy Notes
Power Formula and Applications
Mechanical Energy Examples
NCERT Physics Class 11 Solutions
NEET Physics Formula Sheet
Rotational Motion Notes
Gravitation Complete Notes
Oscillations and SHM Notes
Units and Measurements Notes
NEET Physics MCQs with Answers
FAQ QUESTIONS
Q1. What is kinetic energy?
A. Kinetic energy is the energy possessed by a body due to its motion.
Q2. What is the formula of kinetic energy?
A. K = 1/2 mv².
Q3. What is work done by a variable force?
A. Work done by a variable force equals the area under the force-displacement graph.
Q4. Why is speed not reduced by 90% when kinetic energy becomes 10%?
A. Because kinetic energy is proportional to the square of speed.
Q5. What is the SI unit of work?
A. Joule (J).
WORK, ENERGY AND POWER
1. Kinetic Energy (K)
Kinetic energy is the energy possessed by a body due to its motion.
Where:
- m = mass of the object
- v = speed of the object
- K = kinetic energy
2. Typical Kinetic Energies
| Object | Mass (kg) | Speed (m/s) | Kinetic Energy (J) |
|---|---|---|---|
| Car | 2000 | 25 | 6.3 × 10⁵ |
| Running Athlete | 70 | 10 | 3.5 × 10³ |
| Bullet | 0.05 | 200 | 10³ |
| Stone Dropped from 10 m | - | 14 | 10² |
| Rain Drop | 3.5 × 10⁻⁵ | 9 | 1.4 × 10⁻³ |
| Air Molecule | ≈ 10⁻²⁶ | 500 | ≈ 10⁻²¹ |
3. Example: Bullet Passing Through Plywood
Given:
- Mass of bullet = 50 g = 0.05 kg
- Initial speed = 200 m/s
- Final kinetic energy = 10% of initial kinetic energy
Step 1: Initial Kinetic Energy
Ki = ½ × 0.05 × (200)²
Ki = 1000 J
Step 2: Final Kinetic Energy
Kf = 10% of 1000
Kf = 100 J
Step 3: Calculate Final Speed
vf = √(2 × 100 / 0.05)
vf = 63.2 m/s
4. Important Concept for NEET
Kinetic Energy is proportional to the square of speed.
If kinetic energy becomes 10%:
vf = 0.316 × vi
Speed becomes 31.6% of original speed.
Reduction in speed:
5. Work Done by a Variable Force
Constant Force
A constant force is a force whose magnitude and direction remain unchanged.
Examples:
- Weight of a body near Earth
- Pushing a box with constant force
Where:
- W = Work Done
- F = Force
- s = Displacement
Variable Force
A variable force changes with position, time, or direction.
Examples:
- Spring Force
- Gravitational Force
- Electric Force
6. Small Displacement Method
Consider a very small displacement Δx.
Over this tiny distance, force can be treated as constant.
Where:
- ΔW = Small work done
- F(x) = Force at position x
- Δx = Small displacement
7. Total Work Done
Adding work done over many small intervals:
This is called summation.
Meaning:
- Divide motion into many small parts.
- Find work done in each part.
- Add all the small works.
8. Graphical Interpretation
In a Force vs Position graph:
- Y-axis → Force F(x)
- X-axis → Position x
Area of one small rectangle:
Since:
Therefore:
9. Integral Form of Work Done
When Δx becomes extremely small:
Limits:
Where:
- xi = Initial Position
- xf = Final Position
10. NEET Quick Revision
Kinetic Energy
K = ½mv²
- KE ∝ Mass
- KE ∝ Speed²
If Speed Doubles
K → 4K
If Speed Triples
K → 9K
Variable Force
ΔW = F(x)Δx
W = ΣF(x)Δx
W = ∫F(x)dx
Most Important NEET Statement
✔ Work Done = Area under Force-Displacement Graph
Frequently Asked Relation
If KE becomes n times:
If speed becomes n times:
CBSE Class 11 Physics Question Bank
Chapter: Work, Energy and Power
Section A: Very Short Answer Questions (1 Mark)
Section B: Short Answer Questions (2 Marks)
= ½ × 4 × 25
= 50 J
| Constant Force | Variable Force |
|---|---|
| Remains unchanged | Changes with position |
| W = Fs | W = ∫Fdx |
| Example: Weight | Example: Spring Force |
Therefore kinetic energy becomes four times.
Section C: Long Answer Questions (5 Marks)
Using F = ma
W = mas
Using equation of motion:
v² − u² = 2as
a = (v² − u²)/2s
Substituting:
W = m(v² − u²)/2
For u = 0:
K = ½mv²
ΔW = F(x)Δx
Adding all small works:
W = ΣF(x)Δx
As Δx approaches zero:
W = ∫F(x)dx
Thus, work done by a variable force equals the area under the force-displacement graph.
Section D: Multiple Choice Questions
- A. Mass only
- B. Velocity only
- C. Mass and velocity
- D. Mass and square of velocity
- A. Newton
- B. Joule
- C. Watt
- D. Pascal
- A. 3 times
- B. 6 times
- C. 9 times
- D. 27 times
- A. Velocity
- B. Momentum
- C. Work done
- D. Acceleration
Section E: Assertion and Reason
Reason (R): K = ½mv².
Reason (R): ΔW = FΔx.
Section F: Fill in the Blanks
- Kinetic energy is measured in Joule.
- The formula of kinetic energy is ½mv².
- Work done by variable force equals the area under F-x graph.
- Kinetic energy is proportional to the square of velocity.
- The SI unit of work is Joule.
Section G: Match the Columns
| Column A | Column B |
|---|---|
| Kinetic Energy | Energy due to motion |
| Joule | Unit of work |
| Variable Force | Spring force |
| Area under F-x graph | Work done |
A → Energy due to motion
B → Unit of work
C → Spring force
D → Work done
Section H: Statement Based Questions
Statement II: Kinetic energy depends on square of velocity.
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