Question

Three non-zero forces, F1, F2 , and F3, are acting on an object. Forces F1 and F3 have opposite direction, and both are perpendicular to F2. Under which conditions, if any, will the object be in equilibrium?

a.The magnitudes of F1 and F3 must be equal, and must be one half the magnitude of F2.

b.The magnitudes of F1 and F3 must be equal, and must be one third the magnitude of F2.

c.The magnitudes of F1, F2, and F3 must be equal.

d.no equilibrium

Answer 1

Option d. no equilibrium

Step-by-step explanation:

There are no conditions for the object is in equilibrium.

For the object to be in equilibrium, the sum of the vertical components must be equal to zero and the sum of the horizontal components must be equal to zero.

If we find the sum of the forces in the direction x we have:

`F_1-F_3 + F_2cos(90) = 0`

But
`cos(90) = 0`.

Then
`F_1 = F_3`

If we find the sum of the forces in the axis and we have:

`F_2 + F_1cos(90) - F_3cos(90) = 0`

But
`cos(90) = 0`

So:

`F_2 = 0`

But we know that none of the three forces equals 0. Then the object will not be in equilibrium.

Therefore the answer is option d