Suppose you stand on a bathroom scale and it reads 580.0 N (about 130 lbs). Afterwards, a giant vacuuum machine sucks all the air out of the room. Would the scale reading increase, decrease, or remain the same

the reading of the balance must decrease

Explanation:

The balance of the span is within a fluid the air, for which it is subjected to the pressure of the same, if we write the equilibrium equation we have

          F_net = B -W - F_armosphere

in this case F_net = 540 N

where the thrust is given by Archimedes' principle which states that the thrust is equal to the weight of the fluid dislodged

          B = ρ g V

in this case the density of the air is

           ρ = 1.1 kg / m³

therefore the value of the thrust is small

the force of the air is

            P = F / A

            F = P A

the air pressure is approximately P = 1 10⁵ Pa

Thus

      B <F_atmosphere

Now we can analyze what happens when we remove the air from the room, the pressure at atmospheric pressure decreases therefore the force of the air decreases, while there is some air the thrust is maintained even when it also decreases since the density of the air decreases when decreasing the Pressure.

Consequently, the reading of the balance changes depending on how the thrust and the air force decreases, in general the air force decreases much faster than the thrust, therefore the reading of the balance must decrease

f=ma newton's second law 7x8=56n

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