Question

The resultant of two forces each of magnitude F acting at a point is root F. What is the angle between the vectors ?

Answer 1

Hey.

Here is the answer.

According to the question ,

√F is the resultant force.

Let the angle be x°

As, resultant force = √( F^2 + F^2 +2 F^2 cos x )

√F = √( F^2 + F^2 +2 F^2 cos x )

or, F = F^2 + F^2 +2 F^2 cos x

or, F = 2 F^2 + 2F^2 cos x

or, F = 2F^2(1+ cos x)

or, 1 = 2F ( 1+ cos x)

or, 1/2F = 1+ cos x

or, 0.5 F = 1 + cos x

or , 0.5 F - 1 = cos x

or, x = cos ^-1 (0.5F - 1)

Thanks.

Answer 2

let the angle between them be y

resultant force = √( F^2 + F^2 +2 F^2 cos y )

√F = √( F^2 + F^2 +2 F^2 cos y )

F = F^2 + F^2 +2 F^2 cos y

F = 2 F^2 + 2F^2 cos y

F = 2F^2(1+ cos y)

1 = 2F ( 1+ cos y)

1/2F = 1+ cos y

1/2 F = 1 + cos y

1/2 F - 1 = cos y

y = cos ^-1 (1/2F - 1)