What metal is the object 2 made of? Your answer should be based on your measured

Question

What metal is the object 2 made of? Your answer should be based on your measured data, not, by guess. A beauty crown is made of a pure precious metal. The crow n has a weight of 1.029 N in air and 0.931 N when it is submerged in water. What metal is the crown made of? The plastic block used in Measurement #3 is dropped into water in a beaker. According to Archimedes' principle, the plastic block experiences an upward buoyant force. If the beaker with water and the plastic block were weighted, would the measured total weight be less than the sum of the weights of individual components? Explain it.

Explanation / Answer

2)

The "weight" that you are measuring is really the normal force. Not the true weight, m*g, of the object.

Your force balance on this crown is:
B + N = m*g

Buoyancy + Normal force = Weight (mass*gravitational field)

For air:
B1 + N1 = m*g

For water:
B2 + N2 = m*g

Because the crown is fully immersed, the buoyancy force comes directly from the weight of a parcel of the background fluid, equal in volume to water.

B1 = rho1*V
B2 = rho2*V

Thus:
rho1*V*g + N1 = m*g
rho2*V*g + N2 = m*g

We know N1, N2, rho1, rho2, and g. We need to find m and g. Two equations, two unknowns.
N1 = 1.029 N
N2 = 0.931 N
rho1 = 1.2 kg/m^3
rho2 = 1000 kg/m^3
g = 9.8 N/kg

Ans :-
m = 0.105 kg
V = 0.00001001 m^3
rho = m/v = 10490 kg/m^3

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