Potential Energy of a Spring Notes for NEET 2026 | Hooke's Law Explained

-  Dr.Sanjaykumar pawar 

Potential Energy of a Spring Class 11 Physics Notes for NEET

Potential Energy of a Spring explained with Hooke's Law, formulas, graphs, and NEET exam shortcuts.

Internal Links

• Work, Energy and Power Complete Notes
• Work Done by Variable Force
• Conservative and Non-Conservative Forces
• Kinetic Energy Theorem
• Power and Efficiency
• Mechanical Energy Conservation
• Circular Motion Notes
• Simple Harmonic Motion (SHM)
• Oscillations Complete Notes
• Elasticity and Stress-Strain
• Rotational Motion Notes
• Gravitation Notes
• Laws of Motion 
• Motion in One Dimension
• Motion in Two Dimensions
• Friction Notes
• NCERT Class 11 Physics Notes
• NEET Physics Formula Handbook
• NEET Physics MCQs with Solutions
• Previous Year NEET Physics Questions

NEET Physics Notes

Potential Energy of a Spring (Hooke's Law)

1. Introduction

A spring is an elastic object that returns to its original shape after stretching or compressing.

Examples

• Pen Spring
• Vehicle Shock Absorber
• Spring Balance
• Toy Spring

NEET Point: Spring force is a restoring force.

2. Hooke's Law

The restoring force of a spring is directly proportional to the displacement from its equilibrium position.

F = -kx

Symbol	Meaning	SI Unit
F	Restoring Force	Newton (N)
k	Spring Constant	N/m
x	Displacement	m

Negative sign shows that the spring force always acts opposite to displacement.

3. Spring Constant (k)

The spring constant measures the stiffness of a spring.

Large k	Small k
Hard Spring	Soft Spring

SI Unit

N/m

Dimension

M T^-2

4. Force-Displacement Graph

The graph between force and displacement is a straight line passing through the origin.

Slope = -k

Area under the Force-Displacement graph gives the work done.

5. Work Done by External Force

To stretch the spring slowly from 0 to x, the external force acts in the same direction as displacement.

F = kx

Work done

W = ∫F dx

W = ½kx²

This energy gets stored as Potential Energy inside the spring.

6. Work Done by Spring

Since spring force acts opposite to displacement, its work is negative.

W = -½kx²

External Force → Positive Work

Spring Force → Negative Work

16. NEET Practice MCQs

1. According to Hooke's law, spring force is
   • A. Constant
   • B. Proportional to displacement ✔
   • C. Inversely proportional to displacement
   • D. Zero
   Answer: B
2. The SI unit of spring constant is
   • A. N
   • B. J
   • C. N/m ✔
   • D. Nm
   Answer: C
3. Potential energy stored in a spring is
   U = ½kx²
4. At equilibrium position,
   • A. KE Maximum ✔
   • B. PE Maximum
   • C. Both Zero
   • D. Speed Zero
5. Total mechanical energy is
   • A. Variable
   • B. Constant ✔
   • C. Infinite
   • D. Zero

17. Assertion – Reason Questions

Q1.

Assertion: Spring force is a restoring force.

Reason: Spring force acts opposite to displacement.

Both Assertion and Reason are true, and Reason correctly explains Assertion.

---

Q2.

Assertion: Potential energy is zero at equilibrium.

Reason: Displacement is zero.

Both are true.

18. Previous Year NEET Questions

Question 1

A spring is stretched by x. Potential energy becomes

• A. kx
• B. kx²
• C. ½kx² ✔
• D. 2kx²

---

Question 2

The slope of Force-Displacement graph equals

• A. k
• B. -k ✔
• C. 1/k
• D. Zero

19. One Minute Revision

Concept	Formula
Hooke's Law	F = -kx
Potential Energy	½kx²
Work by Spring	-½kx²
Mechanical Energy	K + U
Maximum Speed	xₘ√(k/m)
Maximum Compression	v√(m/k)

20. Quick NEET Tips

• Remember the negative sign in Hooke's law.
• Potential energy depends on x².
• Spring force always opposes displacement.
• KE is maximum at mean position.
• PE is maximum at extreme positions.
• Total mechanical energy remains constant.
• Hooke's law is valid only within the elastic limit.
• Area under F-x graph represents work done.

NEET Physics Notes

Potential Energy of a Spring

Prepared for Beginners

Happy Learning 📘

16. NEET Practice MCQs

CBSE Class 11 Physics

Chapter: Work, Energy and Power

Topic: Potential Energy of a Spring (Hooke's Law)

---

1. Multiple Choice Questions (MCQs)

1. The restoring force of a spring is
   A) kx
   B) -kx
   C) x/k
   D) k/x

   Answer: B

2. SI unit of spring constant is
   A) N
   B) J
   C) N/m
   D) Nm

   Answer: C

3. Potential energy stored in a spring is
   A) kx
   B) k/x
   C) ½kx²
   D) k²x

   Answer: C

4. At equilibrium position, spring potential energy is
   A) Maximum
   B) Minimum
   C) Infinite
   D) Negative

   Answer: B

5. Hooke's law is valid only within
   A) Elastic limit
   B) Plastic limit
   C) Breaking point
   D) Melting point

   Answer: A

---

2. Very Short Answer Questions (1 Mark)

1. State Hooke's Law.

   Within elastic limit, restoring force is directly proportional to displacement.

2. Write the formula of spring force.

   F = -kx

3. What is the SI unit of spring constant?

   Newton per metre (N/m)

4. Write the formula of spring potential energy.

   U = ½kx²

5. At which position is kinetic energy maximum?

   At the equilibrium position.

---

3. Short Answer Questions (2–3 Marks)

1. Why is the spring force negative?

   The negative sign shows that the restoring force acts opposite to the displacement and always tries to bring the spring back to equilibrium.

2. Derive the expression for work done by stretching a spring.

   W = ∫Fdx = ∫kx dx = ½kx²

3. Define spring constant.

   Spring constant is the force required to produce unit displacement in a spring.

---

4. Long Answer Questions (5 Marks)

1. Derive the expression for the potential energy stored in a spring.

   Given, F = kx Work done, W = ∫Fdx = ∫kx dx = ½kx² Hence, Potential Energy, U = ½kx²

2. State and explain conservation of mechanical energy in a spring block system.

   Total Energy E = K + U = ½mv² + ½kx² The total mechanical energy remains constant.

---

5. Assertion and Reason

Q1.

Assertion (A): Spring force is a restoring force.

Reason (R): Spring force always acts opposite to displacement.

Answer: Both Assertion and Reason are true and Reason correctly explains Assertion.

Q2.

Assertion: Potential energy of spring is maximum at equilibrium.

Reason: Velocity is maximum at equilibrium.

Answer: Assertion is False, Reason is True.

---

6. Fill in the Blanks

1. Spring force is ______ proportional to displacement.

   Directly

2. Hooke's law is F = ______

   -kx

3. Potential energy stored in spring is ______

   ½kx²

4. The SI unit of spring constant is ______

   N/m

5. Mechanical energy is the sum of kinetic and ______ energy.

   Potential

---

7. True / False

1. Spring force always acts opposite to displacement.

   True

2. Potential energy is maximum at equilibrium.

   False

3. Hooke's law is valid within elastic limit.

   True

4. Spring constant is measured in joule.

   False

---

8. Match the Columns

Column A	Column B
Hooke's Law	F = -kx
Spring Potential Energy	½kx²
SI Unit of k	N/m
Equilibrium Position	PE = 0

---

9. Case Study Questions

A block is attached to a spring fixed at one end. The block is pulled by 20 cm and released. The spring constant is 200 N/m.

Q1. Write Hooke's law.

F = -kx

Q2. Calculate potential energy stored.

x = 0.20 m U = ½kx² = ½ × 200 × (0.20)² = 4 J

Q3. At which position is kinetic energy maximum?

At equilibrium position.

Q4. At which position is potential energy maximum?

At maximum extension or compression.

---

10. Important Formula Sheet

• Hooke's Law: F = -kx
• Work Done: W = ½kx²
• Potential Energy: U = ½kx²
• Total Mechanical Energy: E = K + U
• Maximum Speed: v = xm√(k/m)
• Maximum Compression: x = v√(m/k)

---

End of Question Bank

Common Forces in Mechanics Class 11 Notes | NEET & CBSE Physics Guide

 All Forces in Mechanics Explained Simply | Spring, Friction, Tension, Gravity

Common Forces in Mechanics (NEET Level) – Notes

Diagram showing different types of forces in mechanics: gravity, friction, tension, normal force, spring force, and buoyant force.

1. Introduction to Common Forces in Mechanics

Text: In mechanics, we encounter several kinds of forces.

Notes:

• In mechanics (study of motion), many types of forces act on objects.
• These forces cause objects to move, stop, accelerate, or change direction.

---

2. Gravitational Force

Text: The gravitational force is, of course, pervasive.

Notes:

• Gravitational force acts everywhere around us.
• Every object having mass experiences gravity.

---

Text: Every object on the earth experiences the force of gravity due to the earth.

Notes:

• Earth pulls all objects towards its center.
• This pull is called gravitational force.
• It gives an object its weight.

Formula:

W = mg

Where:

• = Weight
• = Mass
• = Acceleration due to gravity ()

---

Text: Gravity also governs the motion of celestial bodies.

Notes:

• Gravity keeps planets around the Sun.
• It keeps the Moon around the Earth.
• It controls the motion of stars, planets, and satellites.

---

Text: The gravitational force can act at a distance without the need of any intervening medium.

Notes:

• Gravity is a non-contact force.
• Objects do not need to touch each other.
• Example: Earth attracts the Moon even though there is empty space between them.

---

3. Contact Forces

Text: All the other forces common in mechanics are contact forces.

Notes:

• Most forces in mechanics act only when two objects touch each other.
• Such forces are called contact forces.

Examples:

• Normal force
• Friction
• Tension
• Buoyant force
• Air resistance

---

Text: A contact force on an object arises due to contact with some other object: solid or fluid.

Notes:

• Contact force appears only when two bodies touch.
• The second body can be:
  • Solid (table, wall)
  • Fluid (water, air)

---

4. Mutual Contact Forces and Newton's Third Law

Text: When bodies are in contact, there are mutual contact forces satisfying the third law.

Notes:

• When two bodies touch, each exerts a force on the other.
• These action-reaction forces are equal and opposite.

Newton's Third Law:

F_{AB} = -F_{BA}

Example:

• Book pushes table downward.
• Table pushes book upward.

---

5. Normal Reaction Force

Text: The component of contact force normal to the surfaces in contact is called normal reaction.

Notes:

• "Normal" means perpendicular to the surface.
• The force exerted by a surface on an object is called Normal Reaction (N).

Example:

• A book resting on a table.
• Table pushes the book upward.

Important:

• Normal force always acts perpendicular to the surface.

---

6. Frictional Force

Text: The component parallel to the surfaces in contact is called friction.

Notes:

• Friction acts parallel to the contact surface.
• It opposes relative motion or tendency of motion.

Example:

• When you push a box, friction opposes its movement.

Direction:

• Always opposite to motion or attempted motion.

---

7. Contact Forces in Fluids

Text: Contact forces arise also when solids are in contact with fluids.

Notes:

• Fluids include liquids and gases.
• Fluids also exert forces on objects touching them.

---

8. Buoyant Force

Text: For a solid immersed in a fluid, there is an upward buoyant force equal to the weight of the fluid displaced.

Notes:

• A fluid pushes an immersed object upward.
• This upward force is called Buoyant Force (Upthrust).

Archimedes' Principle:

F_B = \text{Weight of displaced fluid}

Example:

• Ships float on water.
• A stone feels lighter in water.

NEET Fact:

Buoyant force acts vertically upward.

---

9. Viscous Force and Air Resistance

Text: The viscous force, air resistance, etc. are also examples of contact forces.

Notes:

• Fluids oppose the motion of objects moving through them.

Examples:

1. Air resistance on a falling parachute.
2. Water resistance on a swimmer.

Important:

• These forces act opposite to motion.

---

10. Tension Force

Text: Two other common forces are tension in a string and the force due to spring.

Notes:

• Tension is the force transmitted through a stretched string, rope, or cable.

---

Text: The restoring force in a string is called tension.

Notes:

• When a string is stretched, it tries to return to its original length.
• This pulling force is called tension.

Symbol:

T

Direction:

• Always along the string.
• Always pulls, never pushes.

---

Text: It is customary to use a constant tension T throughout the string.

Notes:

• In an ideal massless string:
  • Tension is the same everywhere.
• Very important assumption in NEET problems.

---

11. Spring Force

Text: When a spring is compressed or extended by an external force, a restoring force is generated.

Notes:

• Stretching or compressing a spring creates a force.
• This force tries to bring the spring back to its natural length.

---

Text: This force is usually proportional to the compression or elongation.

Notes:

• More stretching → more restoring force.
• More compression → more restoring force.

---

Hooke's Law

Text: The spring force F is written as F = – kx.

Notes:

Where:

• = Spring force
• = Spring constant
• = Displacement from natural length

---

Text: The negative sign denotes that the force is opposite to the displacement.

Notes:

• Spring force always acts opposite to stretching or compression.
• It is called a restoring force.

Example:

• Pull spring right → force acts left.
• Compress spring left → force acts right.

---

12. Inextensible String

Text: For an inextensible string, the force constant is very high.

Notes:

• Inextensible means the string cannot stretch significantly.
• Such strings are treated as ideal strings in mechanics.

Assumptions:

• Massless
• Inextensible
• Same tension throughout

---

13. Fundamental Forces and Mechanics

Text: We learnt that there are four fundamental forces in nature.

Notes: There are four fundamental forces:

Force	Range	Importance in Mechanics
Gravitational	Infinite	Important
Electromagnetic	Infinite	Important
Strong Nuclear	Very short	Not used in mechanics
Weak Nuclear	Very short	Not used in mechanics

---

Text: Only the gravitational and electrical forces are relevant in the context of mechanics.

Notes:

• Mechanics mainly deals with:
  1. Gravitational force
  2. Electromagnetic force

---

14. Origin of Contact Forces

Text: The different contact forces of mechanics fundamentally arise from electrical forces.

Notes:

• Normal force, friction, tension, elasticity, etc. are actually due to electromagnetic interactions between atoms.
• Contact forces are not fundamental forces themselves.

Important NEET Point:

All contact forces originate from electromagnetic force.

---

15. Microscopic Explanation

Text: At the microscopic level, all bodies are made of charged constituents (nuclei and electrons).

Notes:

• Matter consists of atoms.
• Atoms contain:
  • Positively charged nuclei
  • Negatively charged electrons

---

Text: Various contact forces can ultimately be traced to electrical forces between charged constituents.

Notes:

• When two objects touch, atoms interact.
• Their charged particles produce electromagnetic forces.
• These appear macroscopically as:
  • Normal force
  • Friction
  • Elastic force
  • Tension

---

16. Why We Study Them Separately

Text: The detailed microscopic origin of these forces is complex and not useful for handling problems in mechanics.

Notes:

• Atomic-level explanations are complicated.
• For solving mechanics problems, we treat forces separately.

Example:

Instead of studying atomic interactions, we simply use:

• Friction formulas
• Tension formulas
• Spring force formulas

---

NEET Quick Revision Table

Force	Contact / Non-contact	Direction
Gravitational Force	Non-contact	Toward Earth
Normal Reaction	Contact	Perpendicular to surface
Friction	Contact	Opposite motion
Tension	Contact	Along string
Spring Force	Contact	Opposite displacement
Buoyant Force	Contact	Upward
Air Resistance	Contact	Opposite motion
Viscous Force	Contact	Opposite motion

Most Important NEET Points

1. Gravity is a non-contact force.
2. Normal reaction acts perpendicular to the surface.
3. Friction acts parallel to the surface.
4. Tension always pulls, never pushes.
5. Spring force follows Hooke's Law.
6. Buoyant force equals the weight of displaced fluid.
7. All contact forces originate from electromagnetic forces.
8. In a massless string, tension is same throughout.
9. Spring force is a restoring force.
10. Weak and strong nuclear forces are generally not used in classical mechanics.

INTERNAL LINKS 

/class-11-physics-laws-of-motion

/friction-detailed-notes-class-11

/tension-in-strings-explained

/hookes-law-spring-force-notes

/buoyant-force-archimedes-principle

/neet-physics-important-topics

/mechanics-formulas-sheet

Common Forces in Mechanics (Mind Map)

• Common Forces in Mechanics
  • 1. Gravitational Force
    • Acts between any two masses
    • Non-contact force
    • Earth pulls all objects (weight = mg)
    • Controls motion of planets, satellites
  • 2. Contact Forces
    • Arise due to physical contact
    • Types:
      • Normal Reaction
        • Acts perpendicular to surface
        • Supports object on surface
      • Frictional Force
        • Acts parallel to surface
        • Opposes motion or tendency of motion
      • Tension Force
        • Acts in strings or ropes
        • Always pulling force
        • Same throughout ideal massless string
      • Spring Force
        • F = -kx (Hooke's Law)
        • Restoring force
        • Opposes displacement
      • Buoyant Force
        • Acts in fluids
        • Equal to weight of displaced fluid
        • Acts upward
      • Air Resistance / Drag
        • Opposes motion in air
        • Depends on speed and shape
      • Viscous Force
        • Opposes motion in liquids
        • Acts like friction in fluids
  • 3. Nature of Forces
    • Gravitational → Non-contact
    • All others → Contact forces
    • Contact forces arise from electromagnetic interaction
  • 4. Fundamental Forces Context
    • Gravitational force → important in mechanics
    • Electromagnetic force → origin of contact forces
    • Strong & weak nuclear → not used in mechanics

Common Forces in Mechanics - Question Bank (Class 11 CBSE)

1. Very Short Answer Questions

1. Q: What is a contact force?
   A: A force that arises due to physical contact between two bodies.
2. Q: Is gravitational force a contact force?
   A: No, it is a non-contact force.
3. Q: Write the formula of spring force.
   A: F = -kx
4. Q: What is tension?
   A: Force transmitted through a stretched string or rope.
5. Q: Direction of normal force?
   A: Perpendicular to the surface.

2. Short Answer Questions

1. Q: Differentiate between contact and non-contact forces.
   A: Contact forces require physical contact (friction, tension), while non-contact forces act without contact (gravity).
2. Q: Define friction and its direction.
   A: Friction is a force that opposes motion. It acts parallel to the surface and opposite to motion.
3. Q: State Hooke’s law.
   A: Within elastic limit, force is proportional to displacement. F = -kx.
4. Q: What is buoyant force?
   A: Upward force exerted by fluid equal to the weight of displaced fluid.

3. Long Answer Questions

1. Q: Explain types of contact forces.
   A: Contact forces include normal force, friction, tension, spring force, buoyant force, viscous force, and air resistance. These arise due to electromagnetic interactions between atoms.
2. Q: Why are contact forces electromagnetic in nature?
   A: All matter consists of charged particles. Interaction between electrons and nuclei produces contact forces like friction and normal reaction.

4. MCQs

1. Q: Which is a non-contact force?
   A. Friction
   B. Tension
   C. Gravity
   D. Normal force
   Ans: C
2. Q: Spring force is given by:
   A. F = kx
   B. F = -kx
   C. F = mg
   D. F = mv
   Ans: B
3. Q: Friction acts:
   A. Perpendicular to surface
   B. Parallel to surface
   C. Vertical upward
   D. None
   Ans: B
4. Q: Buoyant force equals:
   A. Weight of body
   B. Weight of displaced fluid
   C. Mass of body
   D. Volume of body
   Ans: B

5. Assertion and Reason

1. Assertion: Friction opposes motion.
   Reason: It acts parallel to the surface.
   Ans: Both true, but reason is not correct explanation.
2. Assertion: Spring force is restoring force.
   Reason: It acts opposite to displacement.
   Ans: Both true, reason explains assertion.

6. Fill in the Blanks

1. Friction acts ______ to surface. Ans: parallel
2. Normal force is ______ to surface. Ans: perpendicular
3. Spring force follows ______ law. Ans: Hooke’s
4. Tension is always a ______ force. Ans: pulling
5. Buoyant force acts ______ direction. Ans: upward

7. Match the Column

Column A	Column B
Friction	Opposes motion
Spring force	F = -kx
Normal force	Perpendicular support
Buoyant force	Upward force in fluid

8. Case Study

A block is placed on a rough surface. A force is applied but the block does not move initially. When force increases, it starts moving.

1. Q: Why does block not move initially?
   A: Static friction balances applied force.
2. Q: Which force opposes motion?
   A: Frictional force.
3. Q: Type of friction?
   A: Contact force.
4. Q: Direction of friction?
   A: Opposite to motion.

9. Statement Questions

1. Statement: Normal force is always vertical.
   Ans: False
2. Statement: Tension can push and pull.
   Ans: False
3. Statement: All contact forces are electromagnetic in nature.
   Ans: True

COMMON FORCES IN MECHANICS - REVISION SHEET

1. Gravitational Force

• Non-contact force
• Acts between masses
• Formula: W = mg
• Always attractive
• Responsible for weight and planetary motion

2. Contact Forces

• Require physical contact
• Origin: electromagnetic interaction

Types:
• Normal Force: Perpendicular to surface
• Friction: Opposes motion, parallel to surface
• Tension: Force in string, always pulling
• Spring Force: F = –kx (restoring force)
• Buoyant Force: Upward force in fluid = weight of displaced fluid
• Air Resistance: Opposes motion in air
• Viscous Force: Opposes motion in liquids

3. Normal Force

• Acts perpendicular to surface
• Supports object
• Reaction force from surface

4. Friction

• Acts parallel to surface
• Opposes relative motion
• Depends on nature of surfaces

5. Tension

• Force in strings/ropes
• Always pulling
• Same throughout ideal massless string

6. Spring Force

• Hooke’s Law: F = –kx
• Restoring force
• Opposes displacement

7. Buoyant Force

• Acts upward in fluid
• Equal to weight of displaced fluid
• Helps objects float

8. Key Points (VERY IMPORTANT)

• Gravity is non-contact force
• All contact forces are electromagnetic in origin
• Friction opposes motion
• Tension only pulls
• Normal force is perpendicular
• Spring force is restoring in nature