Question

The result of 2 forces, one in which is double the other is 260N. If the direction of larger force is reversed and other remain same, the resultant reduces to 180N. Determine the magnitude of the force and the angle between forces

Answer 1

Explanation:

Let the forces be of magnitude x and 2x. Then, 

x2 +4x2+4x2cosy=(260)2

and similarly 

x2+4x2-4x2cosy=(180)2

Simplifying we get,

10x2=100000 or x=100

and 

8x2cosy=35200

or cosy=44/100

so forces are 100N and 200N and at an angle of somewhere round 64 degrees.

Answer 2

Explanation:

Let the forces be of magnitude x and 2x. Then,

x^2 +4x^2+4x^2cosy=(260)^2

and similarly

x^2+4x^2-4x^2cosy=(180)^2

Simplifying we get,

10x2=100000 or x=100

and

8x2cosy=35200

or cosy=44/100

so forces are 100N and 200N and at an angle of somewhere round 64 degrees.