Buoyancy and Weight of the Fluid Displaced

[theeringirl]

Homework Statement

A 500g mass is submerged in water, displacing 57.6mL of water. The force of gravity on the weight when submerged is measured to be 4.35N. The actual weight should be 4.9N. (remember that the density of water is 1000kg/m³)
(the weight is being held in the water by a spring scale)

(a). Using a "sum of the forces in the y direction" equation, determine the measure of the buoyant force.
(b). Using the volume, calculate the weight of the water displaced.

Homework Equations

(a). ΣFy = F_b + F_scale – F_g = 0
(b). ρ = m/v ... m = ρv

The Attempt at a Solution

(a). ΣF_y = F_b + F_scale – F_g = 0
F_b = F_{g apparent} - F_scale
F_b= 4.35N – 0.55N
F_b = 3.8N
(b). ρ = m/v
m = ρv
m = (1000kg/m3)( 5.76x10-5 m3)
m = 0.0576kg
Fg = mg
Fg = (0.0576kg)(9.80m/s2)
Fg = 0.564N

 

[eladtan]

In your problem the scales show that the mass "weighs" 4.35N, this is the measure of the normal force experienced by the mass.

The normal force is given by:

$$F_N=F_g-F_b=4.9-F_b=0.55N\Rightarrow F_b=0.55N.$$

The second part seems correct.