Question

The angle between directions of forces A and B is 90° where A= 8 dyne and B = 6 dyne. If the resultant
R makes an angle a with Ā then find the value of 'a'?
[16JP110193]
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Answer 1

Explanation:

the angle between two forces is equal to 90 degree

then their resultant will be the diagonal of the rectangle ( according to parallelogram law)

tan alpha would be opp/adjacent which is = 6/8=3/4

so alpha = 37 degree

Answer 2

Answer:

Concept:

Mathematical operations on Vectors. A vector quantity is a force. The dot product can be used to determine the angle between any two vectors, F1 and F2. The angle between the vectors affects the dot product.

Explanation:

Given: The angle between directions of forces A and B is 90°

Where A= 8 dyne and B = 6 dyne.

Find:

If the resultant R makes an angle a with Ā then find the value of 'a'

Solution:

Fx stands for forces perpendicular to the X axis and Fy stands for forces perpendicular to the Y axis. The letters H and V stand for horizontally and vertically, respectively. The rectangular components can be calculated algebraically or graphically, with the force represented as a vector.

         $\begin{aligned}&\tan \alpha=\frac{F_{y}}{F_{x}}\\&\tan \alpha=\left(\frac{6}{8}\right)\\&\tan \alpha= \frac{3}{4}\\& \alpha = 37\end{aligned}$                            $\begin{aligned}|A| &|B|=6 \\\tan \theta &=\frac{F y}{F x} \\\tan \theta &=\frac{6}{6} \\\tan \theta &=1 \\\theta &=\pi / 4\end{aligned}$

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