Physics Mechanics - How to Solve Friction Problems (Static, Kinetic, Two-Block System) – IIT JEE Guide

How to Solve Friction Problems (Static, Kinetic, Two-Block System) – IIT JEE Guide

(For Students & Teachers – Ready-to-Record Script Included)

Introduction

"Master friction problems, and you unlock 8–12 marks in IIT JEE—enough to jump 50+ ranks. From inclined planes to two-block systems, friction decides whether a block moves or stays stuck. Let’s break it down so you never lose marks again."

WHAT YOU NEED TO KNOW FIRST

1. Newton’s Laws of Motion – Especially NLM-1 (equilibrium) and NLM-2 (F = ma).
2. Free-Body Diagrams (FBDs) – How to draw forces on a single block.
3. Basic Trigonometry – Resolving forces along and perpendicular to inclined planes.

(If you’re shaky on any of these, pause and review them first.)

KEY TERMS & FORMULAS

Key Terms

Formulas

1. Static Friction (Variable)
2. fₛ ≤ μₛN
3. fₛ = Static friction (adjusts to match applied force)
4. μₛ = Coefficient of static friction (MEMORISE)

5. N = Normal force

6. Kinetic Friction (Constant)

7. fₖ = μₖN
8. fₖ = Kinetic friction (always opposes motion)
9. μₖ = Coefficient of kinetic friction (MEMORISE)

10. N = Normal force

11. Normal Force on Horizontal Surface

12. N = mg (if no vertical acceleration)
13. m = Mass of object

14. g = Acceleration due to gravity (9.8 m/s², but use 10 for JEE)

15. Normal Force on Inclined Plane

16. N = mg cosθ

17. θ = Angle of inclination

18. Component of Weight Along Incline

19. mg sinθ (driving force down the incline)

STEP-BY-STEP METHOD

(Follow these steps for every friction problem. No exceptions.)

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

• Isolate the object(s).
• Draw all forces:
• Weight (mg, downward)
• Normal force (N, perpendicular to surface)
• Applied force (F, if given)
• Friction (f, opposite to motion or tendency of motion)
• Label angles (if inclined plane).

Step 2: Resolve Forces

• Horizontal surface? → Forces are already aligned.
• Inclined plane? → Resolve mg into:
• mg sinθ (parallel to incline)
• mg cosθ (perpendicular to incline)

Step 3: Determine if Motion is Impending or Actual

• No motion? → Static friction (fₛ ≤ μₛN).
• Motion occurring? → Kinetic friction (fₖ = μₖN).
• Check if applied force > fₛₘₐₓ → If yes, motion starts.

Step 4: Apply Newton’s Laws

• Equilibrium (no acceleration)? → ΣF = 0 (forces balance).
• Acceleration present? → ΣF = ma (net force causes acceleration).

Step 5: Solve for Unknowns

• Use algebra to find f, N, a, or μ.
• Check units (N for force, m/s² for acceleration).

Step 6: Verify Answer

• Does friction oppose motion? (If not, you messed up.)
• Is fₛ ≤ μₛN? (If not, motion should occur.)
• Does the answer make physical sense? (e.g., friction can’t exceed μₛN.)

WORKED EXAMPLES

Example 1 – Basic (Horizontal Surface)

Problem: A 5 kg block is pushed with a 20 N force on a horizontal surface. μₛ = 0.5, μₖ = 0.4. Will the block move? If yes, find its acceleration.

Solution: 1. FBD:
- Weight (mg = 5 × 10 = 50 N, downward)
- Normal force (N = 50 N, upward)
- Applied force (F = 20 N, right)
- Friction (f, left)

1. Check if motion starts:
2. fₛₘₐₓ = μₛN = 0.5 × 50 = 25 N
3. Applied force (20 N) < fₛₘₐₓ (25 N) → No motion.

4. Friction = 20 N (static, balances applied force).

5. Answer:

6. Block does not move.
7. Friction force = 20 N (static).

What we did and why: - We compared the applied force to fₛₘₐₓ to check if motion starts. - Since F < fₛₘₐₓ, friction adjusts to match F (no acceleration).

Example 2 – Medium (Inclined Plane)

Problem: A 10 kg block is placed on a 30° incline. μₛ = 0.6, μₖ = 0.5. Will the block slide? If yes, find its acceleration.

Solution: 1. FBD:
- Weight (mg = 10 × 10 = 100 N, downward)
- Normal force (N = mg cosθ = 100 × cos30° = 50√3 N)
- Component of weight along incline (mg sinθ = 100 × sin30° = 50 N)
- Friction (f, up the incline)

1. Check if motion starts:
2. fₛₘₐₓ = μₛN = 0.6 × 50√3 ≈ 52 N

3. Driving force (50 N) < fₛₘₐₓ (52 N) → No motion.

4. Answer:

5. Block does not slide.
6. Friction force = 50 N (static).

What we did and why: - We resolved mg into components and compared mg sinθ to fₛₘₐₓ. - Since mg sinθ < fₛₘₐₓ, friction prevents motion.

Example 3 – Exam-Style (Two-Block System)

Problem: Two blocks, A (2 kg) and B (3 kg), are in contact on a horizontal surface. A force of 15 N is applied to block A. μₖ = 0.3 for both blocks. Find the acceleration of the system and the contact force between A and B.

Solution: 1. FBD for combined system (A + B):
- Total mass = 2 + 3 = 5 kg
- Applied force (F = 15 N, right)
- Kinetic friction (fₖ = μₖN = 0.3 × (5 × 10) = 15 N, left)
- Net force = 15 N – 15 N = 0 N → No acceleration?
- Wait! This is wrong because friction acts on each block separately.

1. Correct approach: Separate FBDs
2. Block A (2 kg):
   • Applied force (15 N, right)
   • Contact force from B (F_c, left)
   • Friction (fₖ = 0.3 × 20 = 6 N, left)
   • Net force = 15 – F_c – 6 = 2a (Equation 1)

3. Block B (3 kg):

   • Contact force from A (F_c, right)
   • Friction (fₖ = 0.3 × 30 = 9 N, left)
   • Net force = F_c – 9 = 3a (Equation 2)

4. Solve the equations:

5. From Equation 1: 9 – F_c = 2a
6. From Equation 2: F_c – 9 = 3a
7. Add both: 9 – F_c + F_c – 9 = 5a → 0 = 5a → a = 0 m/s²

8. But this contradicts the problem! (We assumed motion, but a = 0 means no motion.)

9. Re-evaluate:

10. Check if motion starts:
    • fₛₘₐₓ for A = 0.3 × 20 = 6 N
    • fₛₘₐₓ for B = 0.3 × 30 = 9 N
    • Total fₛₘₐₓ = 6 + 9 = 15 N
    • Applied force (15 N) = fₛₘₐₓ (15 N) → Motion is impending (just about to start).
11. Since motion is impending, acceleration = 0.

12. Contact force (F_c) = fₖ on B = 9 N.

13. Answer:

14. Acceleration = 0 m/s² (blocks are on the verge of moving).
15. Contact force between A and B = 9 N.

What we did and why: - We initially treated the system as one, but friction acts on each block separately. - We checked if motion starts by comparing F to fₛₘₐₓ. - Since F = fₛₘₐₓ, the blocks are in limiting equilibrium (no acceleration).

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP (Night Before Exam)

"Listen up—friction problems are easy if you follow the steps. First, draw the FBD. Second, resolve forces (especially on inclines). Third, check if motion is happening—if not, friction equals the applied force. If motion starts, use μₖN. For two blocks, draw separate FBDs and solve the equations. Watch out for impending motion—use μₛ, not μₖ. And always, always check if your answer makes sense. Friction can’t be bigger than μₛN, and it always opposes motion. Got it? Now go crush those problems!