Question

Two forces,one of which is double the other has a resultant of 260N. If the direction of the larger force is reversed,the resultant reduces to 180N. Determine the magnitude of the forces and the angle between the forces.

Answer 1

Answer:

Magnitude of the two forces are 100 N and 200 N and the angle between them is 63.9 degree

Explanation:

Let the two forces are F and 2F

now the resultant of the two forces is given as

$F_{net} = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 cos\theta}$

here we have

$260 = \sqrt{F^2 + 4F^2 + 2(F)(2F)cos\theta}$

when larger force is reversed

$180 = \sqrt{F^2 + 4F^2 - 2(F)(2F) cos\theta$

now ratio of two equations

$\frac{260}{180} = \frac{\sqrt{5 + 4cos\theta}}{\sqrt{5 - 4cos\theta}}$

$26^2(5 - 4 cos\theta) = 18^2(5 + 4 cos\theta)$

$1760 = 4000 cos\theta$

$cos\theta = 0.44$

angle between them is given as

$\theta = 63.9 degree$

now we have

$260 = F\sqrt{5 + 4(0.44)}$

$F_1 = 100 N$

$F_2 = 200 N$

#Learn

Topic : Vector addition

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