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

N2- N1 =
`\rho_(w)` V g

Step-by-step 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