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A weightless ladder of length 8 m is resting against a smooth vertical wall and rough horizontal ground

A weightless ladder of length 8 m is resting against a smooth vertical wall and rough horizontal ground as shown in figure. The coefficient of friction between ground and ladder is 0.25. A man of weight 500 N wants to climb up the ladder. Find how much distance along the ladder the man can climb without slip.
Doubtly Asked Student doubt engineering mechanics semester 1 Save WhatsApp Report
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The maximum distance the man can climb without slipping is 6.4 m. This is calculated using the equation:

Friction force = μ × Normal force

Where μ is the coefficient of friction and Normal force is the weight of the man (500 N).

Friction force = 0.25 × 500 N = 125 N

Since the friction force must be equal to or greater than the man's weight, he can climb up to a distance of 6.4 m (125 N/500 N x 8 m).

Doubtly · 15 Oct 2023 Report
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