A ladder of weight W leans against a smooth vertical wall and rests on a rough horizontal floor with a friction coefficient of 1/4. What is the maximum inclination angle to the vertical (expressed as tan-1 x) allowing a man of weight W to safely climb to the top___________________?
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Answer: B. 1/3
Explanation
Equilibrium equations for ladders include normal and frictional floor forces. A man climbing to the top increases overturning moments requiring sufficient friction. Solving static equilibrium yields a maximum angle tangent ratio equal to one third. Static equilibrium requires net force and net torque to equal zero. Smooth walls exert only horizontal forces, while rough floors provide friction. Ladder safety depends heavily on floor friction coefficients and inclination angles.
Industrial safety standards mandate specific ladder angles to prevent workplace falls. Workers must secure ladder bases properly on rough surfaces before climbing upward. Engineering mechanics problems often analyze ladder stability to teach static equilibrium. One fourth matches the given friction coefficient rather than the calculated angle tangent. Three represents the inverse tangent ratio rather than the correct fraction. Four ignores the mechanical advantage calculations involving the climbing person weight.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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