Frequently, attention in an equilibrium situation is confined to a plane. An example would be a ladder leaning against a wall, which is in danger of slipping only in the plane perpendicular to the ground and wall. By orienting a Cartesian coordinate system so that the x and y axes are in this plane, choose which of the following sets of quantities must be zero to maintain static equilibrium in this plane?

a. ∑Fx and ∑τz and ∑Fy
b. ∑Fz and ∑τx and ∑τy
c. ∑τx and ∑Fx and ∑τy and ∑Fy
d. ∑τx and ∑Fx and ∑τy and ∑Fy and ∑τz

To keep a system in equilibrium, the translational equilibrium conditions must be met, which comes from Newton's second law with zero acceleration, let's fix the coordinate system

Σ Fₓ = 0

Σ [tex]F_{y}[/tex] = 0

It must also have rotational equilibrium, which is given by

Σ τ = 0

the bold indicate vector, where torque is

Σ F x r = 0

let's write this expression explicitly for our case

Fₓ y + [tex]F_{y}[/tex] x = 0

remember that the vector product A x B = A B sin θ

Consequently the two products give a vector perpendicular to them, that is, a vector on the z axis, in summary the rotational equilibrium equation is

Σ [tex]\tau_{z}[/tex] = 0

when checking the answers the correct one is a

jayilych4real jayilych4real · Answer 2 · 2021-11-16T19:26:51+01:00

The sets of quantities which must be zero to maintain static equilibrium in this plane are:

a. ∑Fx and ∑τz and ∑Fy

According to the given question, we can see that we need to show the set of quantities which must be zero so that static equilibrium can be maintained on the given plane.

As a result of this, we can see that the set of quantities which must be equals to zero so that static equilibrium can be maintained in the given plane are ∑Fx and ∑τz and ∑Fy.

This is because, for a system to be kept in equilibrium, there would need to be the sum of the forces of all the components of a system would be equals to zero.

Therefore, the correct answer is option A