Question

The resultant of two forces at right angles is 13N. The minimum resultant of the two forces is 7N. the forces are

Answer 1

=> hence ,the forces are 12 and 5 ...

hope this helps you ☺☺☺

Answer 2

Answer:

The forces are 12N and 5N

Explanation:

Let the two forces be A and B.

Let the angle between two forces be θ

The resultant is given as,

$= >R = \sqrt{A {}^{2} + B {}^{2} + 2ABcosθ}$

Given that,the resultant of of two forces at right angles is 13N.Therefore,

$13 = \sqrt{A {}^{2} + B {}^{2} + 0} \\ = > A {}^{2} + B {}^{2} = 169 - - > (1)$

Also given that,the minimum resultant of forces is 7N.The resultant is minimum at θ=180°

$= > 7 = \sqrt{A {}^{2} + B {}^{2} - 2 AB} \\ = > 7 = A - B$

Substituting equation (1) in above term,we get

$7 = \sqrt{169 - 2AB} \\ = > 49 = 169 - 2AB \\ = > AB = 60$

Therefore,

$A + B = \sqrt{A {}^{2} + B {}^{2} + 2AB} = \sqrt{169 + 2 \times 60} = \sqrt{289} = 17$

We now have two main relations

$A + B = 17 \\ A - B = 7$

Solving these two relations,we get

$A = 12 N\: and \: B = 5N$

Therefore,the forces are 12N and 5N

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