Question

piece of cork is held partially submerged in water by a string attached to its bottom....

piece of cork is held partially submerged in water by a string attached to its bottom. The weight of the

cork in air is 20.0 N. The tension in the string is 10.0 N.

(a) What is the buoyant force on the cork? (Newston's 1st law)

(b) What is the volume of the cork under water? (Archimedes Principle)

(c) If this volume is 20.0% of the total volume of the cork, what is the density of the cork?

Oil of density 700 kg/m3 is now poured slowly over the water. The oil forms a layer over the water and surrounds the cork.

(d) The maximum tension the string can bear is 75.0N. When this tension is reached, what is the buoyant force on the cork due to the oil ? (Note that since the cork is tethered by the string, the volume under water is still the same.) [Buoyant force component due to water is the same as in part a]

(e) What percentage of the cork’s volume is in oil? [cork is partly in air, partly in oil & partly in water - not completely coverd by oil- use Force buoyancy from part d to calculate the volume in oil]

(f) The string breaks and the cork floats to the top. The cork is now in contact only with the oil, i.e., it is above the water. What percentage of its volume is in oil? [ cork now floating in oil only]

(a)

Buoyant Force = Weigth of the cork + Tension in the string
Buoyant Force = 20 + 10
Buoyant Force = 30 N

(b)
We know, Buoyant Force Fb = p*g*V
30 = 1000 * 9.8 * V
V = 0.00306 m^3

(c)
20/100 * x = 0.00306
x = 0.0153 m^3

Density = Mass/Volume
p = (20/9.8) / 0.0153
p = 133.4 kg/m^3

(d)
Total Buoyant Force = Weigth of the cork + Tension in the string
Buoyant Force due to oil + Water = 20 + 75
Buoyant Force due to oil + 30 = 95 N
Buoyant Force due to oil = 65 N

please post rest parts in separate post

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