First slide

Vectors

Question

Three forces are acting on a particle as shown in the figure. To have the resultant force only along the Y-direction, the magnitude of the minimum additional force needed is

Moderate

A

0.866 N
B

1.732 N
C

0.5 N
D

4 N

Solution

Resultant is along Y-axis. So, the component of resultant force along X-axis should be zero.
$∴ \sum_{} F_{x} = 0$
or $1 \sin 30^{0} + 2 \sin 30^{0} - 4 \cos 60^{0} + F_{0} = 0$
$∴ F_{o} = \frac{- 1}{2} -1+2 = \frac{1}{2} = 0.5 N$

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