Question

Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. A vertical force of magnitude $100N$ is applied at point $A$ of the frame. Suppose the force is resolved parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $xN$. The value of $x$, to the nearest integer, is ________. $[$Given: $\sin 35°=0.573$, $\cos 35°=0.819$, $\sin 110°=0.939$, $\sin 110°=-0.342]$

Answer 1

Step 1. Given Data,

Two thin massless rods $AB$ and $AC$ as shown in the figure.

A vertical force of magnitude $100N$ is applied at point $A$ of the frame.

The magnitude of the resolved component along the arm $AC$ is $xN$.

Assume, $[$Given: $\sin 35°=0.573$, $\cos 35°=0.819$, $\sin 110°=0.939$, $\sin 110°=-0.342]$

Step 2. The value of $x$, to the nearest integer is,

Component along with AC,

$$\begin{gathered} =F\cos 35°N \\ =100\times 0.819N \\ =81.9N \\ \approx 82N \end{gathered}$$

Hence, The value of $x$, to the nearest integer, is $82N$.