A student in an undergraduate physics lab is studying Archimede\\\'s principle o

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 2.72 kg. The density of this particular alloy of brass is 8.62 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 was submerged in the tank of water. The density of water is 1.00 g/cm3 and the acceleration due to gravity is g = 9.81 m/s2.


v=___________cm^3

t=____________N

Explanation / Answer

First, from the mass and the density, we can calculate the volume of the brass.

The density must be converted to kg/m3. Since there are 1000 grams per kg, and 100 cm per m, we convert 8.62 g/cm3 t0 8620 kg/m3

Then apply = m/V

V = m/ = 2.72/8620

V = 3.16 X 10-4 m3 which is 316 cm3

Next we can calculate the string tension

Tension will be the weight acting down - the bouyant force acting up

T = mg - Vg

T = (2.72)(9.8) - (3.16 X 10-4)(1000)(9.8)

T = 23.6 N

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