Three boys are pulling a heavy trolley by means of three ropes. The boy in the middle is exerting a pull of $100 N$ . The other two boys, whose ropes both make an angle of $30^{o}$ with the central rope, are pulling with forces of $50 \sqrt{3} N$ and $100 \sqrt{3} N$ . Find the magnitude of the resultant pull on the trolley.

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Solution

The $F B D$ for the problem is
Net force in $x -$ direction
$f_{x} = 100 + (100 + 50) (3 \times \frac{\sqrt{3}}{2})$
$f_{x} = 325 N$
Net force in $y -$ direction
$f_{y} = (100 - 50) \frac{\sqrt{3}}{2}$
$f_{y} = 25 \sqrt{3} N$
Net pull $= \sqrt{f_{x}^{2} + f_{y}^{2}}$
$= \sqrt{(325)^{2} + (25)^{2} 3 N}$
$= 327.9 N$

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The FBD for the problem isNet force in x−directionfx=100+(100+50)(3×√32)fx=325 NNet force in y−directionfy=(100−50)√32fy=25√3 NNet pull =√f2x+f2y=√(325)2+(25)23 N=327.9 N