Question

a plastic ball with the volume of 80 cm 3 is attached to the bottom of a container with a string. the container is filled with glycerin so that the sphere will be completely submerged in glycerin. the density of glycerin is 1260kg/m^3. the density of plastic is 840 kg/m^3. what is the tention in the string ?

if you can draw a picture for me so i can understand more...thank you

Answer 1

Fs = force/tension in the string
Fg = gravitational force
Fb = buoyant force
m = mass of the plastic ball
ρ(b) = density of the plastic ball(840 kg/m^3)
ρ(g) = density of glycerine (1260kg/m^3)
V = volume of displaced fluid (which is 1/2 of the rocks volume)

Fs = Fg - Fb
Fs = m*g - ρ(g) * V * g = > (V = 1/2m/ρ(r))
Fs = m*g - ρ(g) * 1/2m/ρ(b) * g

Density of ball = mass/volume

mass of ball = density x volume = 840 *80 *10^-6 kg=0.0672kg
Fs = 0.0672kg * 9,8m/s^2 - (1260kg/m^3 *0.0672) / (2 * 840 kg/m^3) * 9.8m/s^2
Fs = 0.65856 N - 7N
Fs = 0.6534N