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Applying NLM along 3 Axis

In figure, tw...

Question

In figure, two blocks are separated by a uniform strut attached to each block with frictionless pins. Block $A$ weighs $400 N$ , block $B$ weighs $300 N$ , and the strut $A B$ weigh $200 N$ . If $μ = 0.25$ under $B$ , determined the minimum coefficient of friction under $A$ to prevent motion.

0.4

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0.2

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0.8

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0.1

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Solution

The correct option is D $0.4$
Consider $F B D$ of structure.
Applying equilibrium equations,
$A v + B v = 200 N . . . . (i)$
$A_{H} = B_{H} . . . . (i i)$
From $F B D$ of block $B$ ,
$B_{H} + F_{B} cos 60^{\circ} - N_{B} sin 60^{\circ} = 0$
$N_{B} cos 60^{\circ} - B_{V} - 300 + F_{V} sin 60^{\circ} = 0$
$F_{B} = 0.25 N_{B}$
$B_{H} - 0.74 N_{B} = 0 . . . . . (i i i)$
$- B_{V} + 0.71 N_{B} = 300 . . . . . (i v)$
$F B D$ of block $A$
$F_{A} - A_{H} = 0 . . . . . (v)$
$N_{A} - A_{V} = 400$
$F_{A} = μ_{A} N_{A}$
$∴ μ_{A} N_{A} - A_{H} = 0 . . . . . (v i)$
On solving above equations, we get
$N_{A} = 650 N, F_{A} = 260 N, F_{A} = μ_{A} N_{A}$
$∴ μ_{A} = \frac{260}{250} = 0.4$ .

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In figure, two blocks are separated by a uniform strut attached to each block with frictionless pins. Block A weighs 400N, block B weighs 300N, and the strut AB weigh 200N. If μ=0.25 under B, determined the minimum coefficient of friction under A to prevent motion.

In figure, two blocks are separated by a uniform strut attached to each block with frictionless pins. Block $A$ weighs $400 N$ , block $B$ weighs $300 N$ , and the strut $A B$ weigh $200 N$ . If $μ = 0.25$ under $B$ , determined the minimum coefficient of friction under $A$ to prevent motion.