A hollow copper ball floats in the water when fully submerged. What is the equal mass of the ball

| April 21, 2021 | education

A hollow copper ball floats in the water when fully submerged. What is the equal mass of the ball if the volume of the air cavity is 17.75 cm3?

Data: Vpol – the volume of the air cavity (Vpol = 17.75 cm3; in the SI system Vpol = 17.75 * 10-6 m3).

Const: ρCu – copper density (according to the condition ρCu = 8900 kg / m3); ρН2О – density of water (ρН2О = 1000 kg / m3).

1) The volume of copper in the ball.

Since the taken hollow ball floats in water, the equality is true: FA = P.

ρН2О * g * Vsh = msh * g.

ρН2О * (Vpol + VCu) = ρCu * VCu.

1000 * (17.75 * 10-6 + VCu) = 8900 * VCu.

17.75 * 10-6 + VCu = 8.9 * VCu.

7.9 * VCu = 17.75 * 10-6.

VCu = 17.75 * 10-6 / 7.9 ≈ 2.25 * 10-6 m3.

2) Ball mass: msh = ρCu * VCu = 8900 * 2.25 * 10-6 ≈ 20 * 10-3 kg.

Answer: The mass of the ball should be 20 g.



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