Question

A 10kg block of aluminum (p=2700 kg/ m^3) is attached to a rope. Find the tension force in the rope if the block is in vacuum? What is the tension force in the rope if the block is in air (p=1.29 kg/m^3) and What is the tension force if the block is in water?

Answer 1

I. Find the tension force in the rope if the block is in vacuum?

In vacuum medium F_B = 0 because vacuum density = 0.

Rope tension T = F = mg = 10 kg * 9.81 m/s² = 98.1 N.

II. What is the tension force in the rope if the block is in air (p = 1.29 kg/m³)?

V = 10kg / 2700kg/m³ = 0.0037 m³

F_B = 1.29kg/m³ * 9.81m/s² * 0.0037 m³ = 0.047 N.

T = F - F_B = 98.1 - 0.047 = 98.053 N.

III. What is the tension force if the block is in water?

Water density is 1 g/L = 1000 kg/m³.

F_B = 1000 kg/m³ * 9.81m/s² * 0.0037 m³ = 36.3 N.

T = F - F_B = 98.1 - 36.3 = 61.8 N.