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Friction problems look easy until you meet two blocks stacked on each other, and then the question "which way does friction act, and how big is it?" has no obvious answer. Most mistakes come from one habit: writing f = μN every time. This post shows when that is right and when it is wrong, with worked examples for a single block, an incline and two stacked blocks, and a routine to practise with.
What does the syllabus include?
The NTA Syllabus for JEE (Main) 2026 lists "Static and Kinetic friction, laws of friction, rolling friction" under Laws of Motion, and the JEE (Advanced) 2026 Information Brochure lists "Static and dynamic friction". The matching section is in NCERT Class 11 Physics, Chapter 4. Check the current year's syllabus before you plan.
How are static and kinetic friction different?
NCERT puts the two laws side by side:
Static friction, when surfaces do not slide: fₛ ≤ μₛN. It takes whatever value is needed to prevent sliding, up to the limit μₛN.
Kinetic friction, once sliding has begun: fₖ = μₖN, and μₖ is usually less than μₛ.
The inequality is the key. Static friction is a "whatever is needed" force, like the normal force.
Example 1. A 5 kg block rests on a floor with μₛ = 0.5 and μₖ = 0.4. Take g = 10 m/s². You push horizontally with 20 N.
N = mg = 50 N, so the maximum static friction is 0.5 × 50 = 25 N.
Your 20 N is less than 25 N, so the block does not move.
Friction is 20 N, not 25 N, because that is all that is needed.
Now push with 30 N. That exceeds 25 N, so the block slides, kinetic friction is 0.4 × 50 = 20 N, and a = (30 − 20)/5 = 2 m/s².
What is the angle of repose?
Tilt a surface until a block on it just starts to slide. NCERT shows that at that angle, tan θ = μₛ, independent of the block's mass. If μₛ = 0.3, the block starts to slide at θ = tan⁻¹ 0.3 ≈ 16.7°. Below that angle, static friction equals mg sin θ, again only what is needed.
How do you solve blocks on blocks?
Example 2. Block A (2 kg) sits on block B (4 kg). The floor is smooth. Between A and B, μₛ = 0.4 and μₖ = 0.3. A horizontal force F pulls B. Take g = 10 m/s².
Step 1: assume they move together. The only horizontal force on A is friction from B, so A's acceleration comes entirely from friction. The largest it can be is μₛ m_A g / m_A = μₛg = 4 m/s².
Step 2: find the largest F with no slipping. Together, F = (m_A + m_B) a, so F_max = 6 × 4 = 24 N.
Case F = 18 N. 18 is below 24, so they move together with a = 18 / 6 = 3 m/s². Friction on A = m_A a = 2 × 3 = 6 N, below the 8 N limit. Check passed.
Case F = 36 N. 36 is above 24, so A slips on B and kinetic friction acts: 0.3 × 2 × 10 = 6 N.
A: a_A = 6 / 2 = 3 m/s², forward.
B: friction from A acts backward on B, so a_B = (36 − 6) / 4 = 7.5 m/s².
B runs ahead of A, as expected, and friction on A points forward, the direction B moves relative to A.
Why does the free-body diagram matter so much?
Friction direction comes from relative motion between two surfaces, which is easy to get wrong unless each body is drawn separately. In a two-year study, Rosengrant, Van Heuvelen and Etkina (2009) found that "students who draw diagrams correctly are significantly more successful in obtaining the right answer". They also found that high-achieving students used the diagrams to check their work. Friction is a known difficulty: Besson and colleagues (2007) note that "students generally have difficulty understanding friction" and that school courses often give it too little attention.
Common mistakes and how to avoid them
Writing f = μₛN when nothing slides. Static friction is only as large as needed. Use the equations of motion to find it.
Taking N = mg when a force is angled. A pull at angle θ above the horizontal reduces N to mg − F sin θ.
Friction always opposing the applied force. It opposes relative sliding between the two surfaces. On the top block in Example 2, it points forward.
One diagram for both blocks. Draw each block separately, with the friction pair equal and opposite.
If you set up the equations and still get a strange answer, check each step against a worked solution. The Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer. For more on the diagram habit, read our post on drawing the diagram first, and for related errors see common mistakes in mechanics.
A practice routine for this chapter
Day 1: Five single-block questions where the push is sometimes below and sometimes above μₛN. Decide "moves or not" before calculating.
Day 2: Five incline questions, including one where the block is pushed up and one where it is held at rest.
Day 3: Five stacked-block questions with the force on the top block and on the bottom block. Use the assume-then-check method each time.
Day 7: A mixed set of eight, timed, with a separate free-body diagram for every body.
Tonight, redo Example 2 with the 36 N force applied to the top block instead, and check whether the blocks slip.
