Question

In the lab you place a beaker that is half full of water (density pw ) on a scale. You now use a light string to suspend a piece of metal of volume V in the water. The metal is completely submerged, and none of the water spills out of the beaker.
Give a symbolic expression for the change in reading of the scale.Express your answer in terms of the variables pw, V, and appropriate constants.N2-N1=___________

Answer 1

Answer:

N2- N1 = $\rho_{w}$  V g

Explanation:

Let's use for this exercised the equilibrium relationship

        ∑ F = 0

        N -W = 0

        N = W = mg

Let's use density redefinition

       ρ = m / v

       m = ρ V

       N₁ = (ρ V) g

Repeat for when the liquid is submerged, in this case an upward thrust appears as a result of the water dispensed (rgow)

        N₂ + B - W = 0

        N₂ = W - B

        B = $m_{water}$ g

        $\rho_{w}$ = m / V

         $m_{w}$  =  $\rho_{w}$  V

        N = ρ V g -  $\rho_{w}$  Vg

        N2 = N1 +   $\rho_{w}$  V g

        N2- N1 = $\rho_{w}$  V g