Key relationship
Nfloor = mg; Rwall = mg/(2tanθ); μrequired = 1/(2tanθ).
Physics · Class 11
Can the ladder stay balanced?
Taking moments about the foot determines the horizontal wall reaction. The floor must provide equal horizontal friction and support the weight. A steeper ladder needs less friction in this ideal model.
Open the interactive experiment →Can the ladder stay balanced?
சமநிலையில் நிகர விசையும் நிகர திருப்புவிசையும் பூஜ்யம். சுவரின் எதிர்விசையை தரையின் உராய்வு சமப்படுத்த வேண்டும்.
Key notes, relationships and model limits
Remember
Taking moments about the foot determines the horizontal wall reaction. The floor must provide equal horizontal friction and support the weight. A steeper ladder needs less friction in this ideal model.
Common trap
Static friction is the required reaction up to its limit, not always μN.
Model limits
Uniform ladder against a smooth wall on a rough horizontal floor; no person or extra loads. Static equilibrium requires both zero force and zero torque.
What you will learn
Combine translational and rotational equilibrium and test friction feasibility.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
For 20 kg at 60°, N=196.2 N and wall reaction=56.64 N. Thus μrequired=0.289; μ=0.4 can hold it.
Why this matters
The model connects can the ladder stay balanced? with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
At 45°, what minimum floor coefficient holds a uniform ladder at a smooth wall?
- 0.25
- 0.5
- 1.0
Read the explanation
μrequired = 1/(2tan45°) = 0.5.
Course connection: Class XI Chapter 6. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.