Question

The greatest and least resultant of two force acting at point is 10 N and 6N respectively. If each force is increasing by 3N find the resultant of new force when acting in point at angle of 90degress with each other

Answer 1

$\textbf{solution}$
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There are two forces namely F1 and F2 then,

F1 + F2 = 10N

F1 - F2 = 6N

Adding the above two equations we have

2F1 = 16

F1 = 8N

Then we have

F1 + F2 = 10N

8N + F2 = 10N

F2 = 10N - 8N

F2 = 2N

When increased by 3N

F1 = 8N + 3N = 11N

F2 = 2N + 3N = 5N


$Resultant = \sqrt{ {11}^{2} + {5}^{2} } \\ \\ = \sqrt{(11 \times 11) + (5 \times 5)} \\ \\ = \sqrt{121 + 25} \\ \\ = \sqrt{146} \\ \\ = 12.083N \:$

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Answer 2

If two forces are F1 and F2 then,

F1 + F2 = 10N

F1 - F2 = 6N

Add above two equations

2F1 = 16

F1 = 8N

From first equation

F2 = 10 - 8 = 2N

When increased by 3N

F1 = 8N + 3N = 11N

F2 = 2N + 3N = 5N

Resultant = sqrt(11^2 + 5^2) = sqrt(121 + 25) = sqrt(146) = 12.083N