In this example we will see how to determine the buoyant force given the mass an
ID: 1508089 • Letter: I
Question
In this example we will see how to determine the buoyant force given the mass and density of a submerged object. A 15.0 kg solid-gold statue is being raised from a sunken treasure ship, as shown in (Figure 1) . (a) Find the tension in the hoisting cable when the statue is completely immersed. (b) Find the tension when the statue is completely out of the water. A brass statue with a mass of 0.485 kg and a density of 8.00×103kg/m3 is suspended from a string. What is the tension in the string when the statue is completely immersed in water?
Explanation / Answer
1)
a)
given
m = 15 kg
density of gold, rho_glod = 19320 kg/m^3
so, volume of the gold, V = m/rho_glod
= 15/19320
= 7.76*10^-4 m^3
Tension in the cable, T = m*g - B
= m*g - rho_water*V*g
= 15*9.8 - 1000*7.76*10^-4*9.8
= 139.4 N
b) T = m*g
= 15*9.8
= 147 N
2)
m = 0.485 kg
rho_brass = 8*10^3 kg/m^3
volume of statue, V = mass/density
= 0.485/8000
= 6.06*10^-5 m^3
T = m*g - rho_water*V*g
= 0.485*9.8 - 1000*6.06*10^-5*9.8
= 4.16 N
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