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 1.25 kg. The density of this particular alloy of brass is 8.26 g/cm3. 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, ?, of the cylinder and the tension, ?, in the string when it is submerged in the tank of water. The density of water is 1.00 g/cm3, and the acceleration due to gravity is ?=9.81 m/s2.

?=

cm3

?=

N

Answer 1

Sum of forces on cylinder,

T + Bf – W = 0

T = W – Bf = 1.25*9.8 - Bf = 12.25 - Bf

Buoyant force = Density of water in kg/m^3 * g * Volume of displaced water in m^3

= 1000 kg/m^3 *9.81 m/s^2 *Volume of displaced water m^3

= 9810*Volume of displaced water m^3

Volume of cylinder = 1250 g/8.26 g/cm^3 = 151.33*10^-6 m^3

This is the volume of the cylinder and displaced water.

So, we can determine the buoyant force.

Buoyant force = 9810 * 151.33*10^-6

= 1.48 N

T = 12.25 - Bf

= 12.25 - 1.48

= 10.77 N