Question

The diagram shows two forces of equal magnitude acting on an object. If the common magnitude of the forces is 3.6 N and the angle between them is 48°, what third force will cause the object to be in equilibrium?
3.4 N pointing to the right

5.5 N pointing to the right

2.8 N pointing to the right

6.6 N pointing to the right

Answer 1

Answer

6.6 N pointing to the right

Explanation

Given that,

two forces acting of magnitude 3.6N

angle between them = 48°

To find,

the third force that will cause the object to be in equilibrium

1)

Find the vertical and horizontal components of the two forces

vertical force1 = sin(24)(3.6)

vertical force2= -sin(24)(3.6)

(negative sign since it is acting on opposite direction)

vertical force3 = sin(24)(3.6) - sin(24)(3.6)

                        = 0

2)

horizontal force1 = cos(24)(3.6)

horizontal force2= cos(24)(3.6)

horizontal force3 = cos(24)(3.6) + cos(24)(3.6)

                            = 2(cos(24)(3.6))

                            = 6.5775 N

                            ≈ 6.6 N