A smooth circular cylinder of weight W and radius R rests in a V shape groove whose sides are inclined at angles $\propto$ and $\beta$ to the horizontal as shown.

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A smooth circular cylinder of weight W and radius R rests in a V shape groove whose sides are inclined at angles

$\propto$ and

$\beta$ to the horizontal as shown.

written 8.7 years ago by

teamques10 ★ 69k

• modified 4.9 years ago

Find the reactions $R_A$ and $R_B$ at the points of contact.

Alpha (∝) = 20 degrees

Beta (β) = 60 degrees

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engineering mechanics

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written 8.7 years ago by

teamques10 ★ 69k

enter image description here

The above diagram can be redrawn as a free Body Diagram as follows :-

enter image description here

Applying Lami’sTheorem :

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$\dfrac W{\sin⁡(∝+β)}= \dfrac {R_A}{\sin⁡(180-β)}= \dfrac { R_B}{\sin⁡(180-α) } \\ ∴\dfrac W{\sin⁡(20+60)} = \dfrac { R_A}{\sin⁡(180-60) }=\dfrac { R_B}{\sin⁡(180-20) }\\ ∴\dfrac W{\sin⁡(80) } = \dfrac { R_A}{\sin⁡(120) } = \dfrac { R_B}{\sin⁡(160) } \\ ∴ R_A=(\dfrac {\sin120}{\sin 80)}W=0.879W \\ ∴ R_B=(\dfrac {\sin160}{\sin 80)}W=0.347W$

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