The buoyant force is the force up on the sphere exerted by the fluid and down on the fluid by the sphere Nothing is accelerating. The string is still holding the rest of the sphere weight (most of it). Therefore 2.19 N is the buoyant force = rho fluid *g * volume of sphere
g here = 16.58/1.69 = 9.81 m/s^2 so I guess we are on earth.
In other words use 2.19 not 14.39
A sphere of mass of m = 1.69 kg is first placed directly on the plate of an electronic scale. The scale shows 16.58 N as the weight of the object. A large beaker containing a liquid with a density of 783 kg/m^3 is then placed on the scale and the scale is tared (i.e. zeroed to this weight as a reference point, it has a reading of zero with the beaker on the scale). The sphere, hung by a thin string, is lowered into the liquid and submerges below the surface. The scale reads 2.19 N with the sphere not touching the beaker. Calculate the density of the sphere.
My work so far:
F_buoyant = 16.58N - 2.19N = 14.39
F_buoyant = (Rho_liquid)(g)(V_liquid displaced)
14.39N = (783kg/m^3)(9.81m/s^2)(V_liquid displaced)
V_liquid displaced = 0.001873398 m^3 = 0.00187 m^3
So the density of the sphere:
rho_sphere = m_sphere/V_sphere
V_sphere = V_liquid displaced = 0.00187 m^3
rho_sphere = 1.69kg/0.00187m^3
= 902.1040911 kg/m^3
= 902 kg/m^3
... which is what I got for the final answer but apparently it is incorrect. If there is anything, what did I do wrong?
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