Question

A student in an undergraduate physics lab is studying Archimede's principle of bouyancy. The student is given a brass cylinder and, using a triple beam balance, finds the mass to be 3.21 kg. The density of this particular alloy of brass is 8.62 g/cm 3 . The student ties a massless string to one end of the cylinder and submerges it into a tank of water where there is an apparent reduction in the weight of the cylinder. With this information, calculate the volume, V , of the cylinder and the tension, T , in the string when it is submerged in the tank of water. The density of water is 1.00 g/cm 3 , and the acceleration due to gravity is gVolume of the cylinder: _____ cm3Tension in the string: ______ N

Answer 1

V = 0.3724 m³

T = 27.836 N

Step-by-step explanation:

Given :

m = 3.21 kg , W= 3.21 * 9.81 m / s² = 31.4901 N

ρ = 8.62 g / cm ³ = 8620 kg / m³

V = m / ρ = 3.21 kg / 8620 kg / m³

V = 0.3724 m³

when submerged the weight of brass cylinder is equal to the tension in string:

F = (0.3724m³) * (1000 kg / m³) * (9.81 m/s²²) = 3.653 ≈ 3.65 N

T = 31.4901 N - 3.65 N

T = 27.836 N