ABCDE is a pentagon. Forces overrightarrow{AB | vedclass

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Question

(C) Let the resultant of the given forces be $\vec{R}$.$\vec{R} = \overrightarrow{AB} + \overrightarrow{AE} + \overrightarrow{ED} + \overrightarrow{DC

Vedclass · Accepted Answer

$\overrightarrow{BC}$

Vedclass · Answer

(C) Let the resultant of the given forces be $\vec{R}$.$\vec{R} = \overrightarrow{AB} + \overrightarrow{AE} + \overrightarrow{ED} + \overrightarrow{DC}$.Using the triangle law of vector addition,we know that $\overrightarrow{AE} + \overrightarrow{ED} = \overrightarrow{AD}$.Substituting this into the expression for $\vec{R}$,we get $\vec{R} = \overrightarrow{AB} + \overrightarrow{AD} + \overrightarrow{DC}$.Since $\overrightarrow{AD} + \overrightarrow{DC} = \overrightarrow{AC}$,we have $\vec{R} = \overrightarrow{AB} + \overrightarrow{AC}$.We want the final resultant to be $2\overrightarrow{AC}$. Let the force to be added be $\vec{F}$.Then,$\vec{R} + \vec{F} = 2\overrightarrow{AC}$.$(\overrightarrow{AB} + \overrightarrow{AC}) + \vec{F} = 2\overrightarrow{AC}$.$\vec{F} = 2\overrightarrow{AC} - \overrightarrow{AC} - \overrightarrow{AB} = \overrightarrow{AC} - \overrightarrow{AB}$.Using the triangle law,$\overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC}$,which implies $\overrightarrow{BC} = \overrightarrow{AC} - \overrightarrow{AB}$.Therefore,the force to be added is $\overrightarrow{BC}$.

$ABCDE$ is a pentagon. Forces $\overrightarrow{AB}, \overrightarrow{AE}, \overrightarrow{DC}, \overrightarrow{ED}$ act at a point. Which force should be added to this system to make the resultant $2\overrightarrow{AC}$?

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