Problem 1 (5 pts): Archimedes supposedly was asked to determine whether a crown

Question

Problem 1 (5 pts): Archimedes supposedly was asked to determine whether a crown made for the king consisted of pure gold. Legend has it that he solved this problem by weighing the crown first in air and then in water, as shown in the figure below. Suppose the scale read 7.84 N in air and Archimedes found a density of 7840 kg/m2 for the crown. (a) Write the condition of equilibrium for both measurements. (b) Find the magnitude of the buoyant force (B FB)? (c) How much reads the scale when the crown is immersed in water? (2 pts) (2 pts) (1 pt) T2

Explanation / Answer

A)

For equilibrium, the net force on the crown must be 0

For this to happen,

For case A(weighing in the air) :

the weight of the crown must be equal to the spring force

For case B(weighing inside water)

The weight of the crown must be equal to Spring force plus the upthrust(buoyant force) on it .

B)

Magnitude of buoyant force :

B= Density of water*volume*g

here g = acceleration due to gravity = 9.8 m/s2

So, B = 1000*V*9.8

volume of the crown , V = weight of crown in air/(g*density of crown)

= 7.84/(9.8*7840)

= 1.02*10^-4 m3

So, B = 1000*1.02*10^-4*9.8

= 1 N

C)

Scale reading = 7.84 - 1 N = 6.84 N

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