Physics - Mechanics and Properties of Matter - How to Solve: Friction (Static, Kinetic, Block-on-Block, Angle of Repose) – NEET UG Physics Guide

How to Solve: Friction (Static, Kinetic, Block-on-Block, Angle of Repose) – NEET UG Physics Guide

Introduction

"Master friction, and you unlock 3-5 marks in NEET Physics—enough to push you into the top 10%." Friction appears in block-on-block problems, inclined planes, and even circular motion (like a car on a curved road). If you mess this up, you lose marks in mechanics, rotational dynamics, and even biology (e.g., friction in joints). Today, we’ll break it down so you never second-guess a friction question again.

WHAT YOU NEED TO KNOW FIRST

Before diving in, make sure you understand:
1. Newton’s Laws of Motion (especially NLM-1 for equilibrium and NLM-2 for acceleration).
2. Free-Body Diagrams (FBDs) – How to draw forces on an object.
3. Trigonometry on Inclined Planes – Resolving forces into parallel and perpendicular components.

If any of these are shaky, pause here and review them first.

KEY TERMS & FORMULAS

1. Types of Friction

2. Formulas (MEMORIZE THESE)

STEP-BY-STEP METHOD

Follow these exact steps for every friction problem:

Step 1: Draw the Free-Body Diagram (FBD)

• Label all forces:
• Weight (mg) – Always downward.
• Normal Force (N) – Perpendicular to the surface.
• Friction (f) – Parallel to the surface, opposes motion.
• Applied Force (F) – If given (e.g., pushing/pulling).
• On an incline? Resolve mg into:
• mg sinθ (parallel to incline)
• mg cosθ (perpendicular to incline)

Step 2: Determine if the Object is Moving or About to Move

• If moving → Kinetic friction (fₖ = μₖN)
• If at rest → Static friction (fₛ ≤ μₛN)
• If "just about to move" → fₛ = μₛN (maximum static friction)

Step 3: Write Newton’s 2nd Law Equations

• For equilibrium (no acceleration):
• ΣF = 0 (forces balance)
• For acceleration:
• ΣF = ma (net force causes acceleration)
• Choose axes wisely:
• Parallel to surface → Friction, applied force, component of weight.
• Perpendicular to surface → Normal force, component of weight.

Step 4: Solve for Unknowns

• Find N first (usually from perpendicular forces).
• Then find friction (using N and μ).
• Check if friction is static or kinetic (based on motion).

Step 5: Verify Units & Reasonableness

• Friction force ≤ μₛN (if static).
• Friction force = μₖN (if kinetic).
• Normal force ≠ weight (unless on flat surface with no other forces).

WORKED EXAMPLES

Example 1 – Basic (Static Friction on Flat Surface)

Problem: A 5 kg block is at rest on a horizontal surface. A 10 N force is applied horizontally. If μₛ = 0.4, will the block move? If not, what is the friction force?

Solution (Step-by-Step):
1. Draw FBD: - Weight (mg) = 5 × 9.8 = 49 N (downward) - Normal Force (N) = mg = 49 N (upward, since no vertical acceleration) - Applied Force (F) = 10 N (right) - Friction (fₛ) (left, opposes motion)

1. Check if block moves:
2. Maximum static friction (fₛ,max) = μₛN = 0.4 × 49 = 19.6 N

3. Applied force (10 N) < fₛ,max (19.6 N) → Block does NOT move.

4. Friction force = Applied force (since no motion):

5. fₛ = 10 N (balances the push).

What we did and why: - We compared the applied force to the maximum static friction to see if motion occurs. - Since the block doesn’t move, friction adjusts to match the applied force.

Example 2 – Medium (Kinetic Friction on Incline)

Problem: A 2 kg block slides down a 30° incline with μₖ = 0.25. Find its acceleration.

Solution (Step-by-Step):
1. Draw FBD: - Weight (mg) = 2 × 9.8 = 19.6 N (downward) - Normal Force (N) (perpendicular to incline) - Kinetic Friction (fₖ) (up the incline, opposes motion) - Component of weight parallel to incline (mg sinθ) (down the incline)

1. Resolve forces:
2. Perpendicular to incline: N = mg cosθ = 19.6 × cos30° = 16.97 N

3. Parallel to incline: mg sinθ = 19.6 × sin30° = 9.8 N

4. Kinetic friction:

5. fₖ = μₖN = 0.25 × 16.97 = 4.24 N

6. Net force (down the incline):

7. F_net = mg sinθ – fₖ = 9.8 – 4.24 = 5.56 N

8. Acceleration (a = F_net / m):

9. a = 5.56 / 2 = 2.78 m/s²

What we did and why: - We resolved weight into components because the block is on an incline. - Kinetic friction is constant, so we used fₖ = μₖN. - Net force = mg sinθ – fₖ because friction opposes motion.

Example 3 – Exam-Style (Block-on-Block with Friction)

Problem (NEET 2018-Style): Two blocks, A (3 kg) and B (2 kg), are stacked on a horizontal surface. μₛ = 0.3 between A and B, and μₖ = 0.2 between B and the ground. A 15 N force is applied to block B. Will block A slip on B? If not, what is the friction force between A and B?

Solution (Step-by-Step):
1. Draw FBD for both blocks: - Block A (top): - Weight (m_A g) = 3 × 9.8 = 29.4 N (down) - Normal Force (N_A) = 29.4 N (up, from B) - Friction (f_A) (horizontal, opposes relative motion) - Block B (bottom): - Weight (m_B g) = 2 × 9.8 = 19.6 N (down) - Normal Force (N_B) = m_A g + m_B g = 49 N (up, from ground) - Applied Force (F) = 15 N (right) - Friction from ground (f_B) (left, opposes motion) - Friction from A (f_A) (left, Newton’s 3rd Law)

1. Check if A slips on B:
2. Maximum static friction between A and B (f_A,max) = μₛ N_A = 0.3 × 29.4 = 8.82 N
3. Acceleration of system (if no slipping):
   • Total mass = 3 + 2 = 5 kg
   • Net force = F – f_B = 15 – μₖ N_B = 15 – (0.2 × 49) = 15 – 9.8 = 5.2 N
   • a = F_net / m_total = 5.2 / 5 = 1.04 m/s²
4. Friction force needed to accelerate A (f_A = m_A a = 3 × 1.04 = 3.12 N)

5. 3.12 N < 8.82 N → A does NOT slip on B

6. Friction force between A and B = 3.12 N (static, not maximum).

What we did and why: - We treated the system as a whole first to find acceleration. - Then, we checked if the required friction exceeds the maximum static friction. - Since f_A < f_A,max, the blocks move together (no slipping).

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP (Night Before Exam)

"Listen up—this is friction in 60 seconds."

1. Static friction (fₛ) adjusts up to μₛN—it’s not always μₛN, only when the object is just about to move.
2. Kinetic friction (fₖ) is always μₖN—constant once sliding starts.
3. On an incline, N = mg cosθ—not mg! Weight splits into mg sinθ (down slope) and mg cosθ (into slope).
4. Angle of repose = tanθ = μₛ—memorize this, NEET loves it.
5. Block-on-block? Check if the top block slips by comparing required friction vs. μₛN.
6. Always draw FBDs—label N, mg, friction, and applied forces.
7. If stuck, ask: Is the object moving? If yes → kinetic. If no → static.

"Now go crush that friction question! ?