A block of mass is placed on a surface having vertical cross section given by . If coefficient of friction is , the maximum height above the ground at which block can be placed without slipping is:

Question

A block of mass  is placed on a surface having vertical cross section given by . If coefficient of friction is , the maximum height above the ground at which block can be placed without slipping is:

Canvas Classes · Accepted Answer

🧠 Curved Surface → Local Slope =  at Threshold

Read the question. Block on curved surface , . Find max height the block can sit at without slipping.

This is the same template as NLM-097 (with slightly different language). The principle: at the threshold of slipping, the local slope of the surface equals  (the angle of repose).

Slope of : .

At threshold: .

Corresponding height: .

🗺️ Working It Out

(See above.)

The mental model: at any point on the curve, the surface is locally an inclin

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