Read before you solve · 3 min
Read Friction at an Angle: Optimise the Normal Reaction
An upward pull lowers the normal reaction and therefore the limiting friction. The best angle balances horizontal pull against this reduction.
NSEP · Laws of Motion · 1 linked question · 100% coverage
Know this first
Motion and force questions become simpler when direction, starting condition, time and the acting forces are marked first.
Distance · Length of the path travelledDisplacement · Straight-line change in positionResultant force · Net force including direction
Study deeper: NCERT Physics · Laws of Motion
Start with the condition
At impending motion, F cos
Rearrange F and maximise the denominator cos θ plus μ sin θ.
Build the governing relation
The optimum has tan
θ = μ, so check that the chosen force remains a pulling—not pushing—force
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
OlympIQ trap
Using F = μ W/cos θ assumes the normal reaction stays W and misses the benefit of the upward component.
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