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, determine the minimum coefficient of friction under A to prevent motion.

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, determine the minimum coefficient of friction under A to prevent motion. (A) 0.4 (B) 0.2 (C) 0.8 (D) 0.1

Tardigrade Admin · Accepted Answer

Consider FBD of structure.
Applying equilibrium equations,

A v + B v = 200 N

...(i)

A_{H} = B_{H}

...(ii)
From

FB D

of block

B

,

B_{H} + F_{B} cos 6 0^{\circ} - N_{B} sin 6 0^{\circ} = 0

N_{B} cos 6 0^{\circ} - B_{v} - 300 + F_{B} sin 6 0^{\circ} = 0

N_{B} cos 6 0^{\circ} - B_{v} - 300 + F_{B} sin 6 0^{\circ} = 0

F_{B} = 0.25 N_{B} = 0

B_{H} - 0.74 N_{B} = 0

...(iii)

- B_{v} + 0.71 N_{B} = 300

...(iv)

F_{A} - A_{H} = 0

N_{A} - A_{V} = 400

...(v)

F_{A} = μ_{A} N_{A}

∴ μ_{A} N_{A} - A_{H} = 0

...(iv)
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

Q. 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, determine the minimum coefficient of friction under A to prevent motion.

0.4

0.2

0.8

0.1

Q. 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 $B$ , determine the minimum coefficient of friction under $A$ to prevent motion.