Mr. A, B and C are trying to put a heavy pist | vedclass

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Question

(A) To drop the piston vertically into the cylinder,the net horizontal force acting on the piston must be zero.Let the horizontal direction to the rig

Vedclass · Accepted Answer

$\sqrt{3} F_1 = F_2 + 2 F_3$

Vedclass · Answer

(A) To drop the piston vertically into the cylinder,the net horizontal force acting on the piston must be zero.Let the horizontal direction to the right be positive.$1$. The force $F_1$ (from Mr. $A$) acts at an angle of $60^{\circ}$ with the vertical. Its horizontal component is $F_1 \sin 60^{\circ}$ directed towards the left.$2$. The force $F_2$ (from Mr. $B$) acts at an angle of $60^{\circ}$ with the horizontal. Its horizontal component is $F_2 \cos 60^{\circ}$ directed towards the right.$3$. The force $F_3$ (from Mr. $C$) acts horizontally towards the right.For equilibrium in the horizontal direction:$\sum F_x = 0$$F_2 \cos 60^{\circ} + F_3 = F_1 \sin 60^{\circ}$Substituting the values $\cos 60^{\circ} = \frac{1}{2}$ and $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$:$\frac{F_2}{2} + F_3 = F_1 \frac{\sqrt{3}}{2}$Multiplying the entire equation by $2$:$F_2 + 2 F_3 = \sqrt{3} F_1$Thus,the correct relation is $\sqrt{3} F_1 = F_2 + 2 F_3$.

Mr. $A, B$ and $C$ are trying to put a heavy piston into a cylinder at a mechanical workshop in a railway yard. If they apply forces $F_1, F_2$ and $F_3$ respectively on ropes,then for which set of forces at that instant will they be able to perform the said job?

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