A 1.00 103-kg cube of aluminum is placed in a tank. Water is then added to the t

Question

A 1.00 103-kg cube of aluminum is placed in a tank. Water is then added to the tank until half the cube is immersed. (a) What is the normal force on the cube? (See Figure (a).) (b) Mercury is now slowly poured into the tank until the normal force on the cube goes to zero. (See Figure (b).) How deep is the layer of mercury? Assume a very thin layer of fluid is underneath the block in both parts of the figure, due to imperfections between the surfaces in contact.

**************I have these answers for above. Please help me with below*********************

(a) What is the normal force on the cube? (See Figure (a).)

(b) Mercury is now slowly poured into the tank until the normal force on the cube goes to zero. (See Figure (b).) How deep is the layer of Mercury?

Explanation / Answer

Normal force = N = mg - B
B = (density of water)*(vlume displaced)
but volume displaced = 0.5*volume of aluminium = 0.5*mass/desity
B = (1000)*0.5*1000/2830 = 176.6784 N
N = 1000*9.8 - B = 9623.321 N

N = 0
so B = mg = 9800 N = (density of water)*(vloume displaced) + (density of mercury)*volume displaced
B = 1000*0.5*1000/2830 + 13594*V = 9800
V = 0.7079 m^3
but V = l^2*h [ where l^3 = 1000/2830]
h = 1.16 m

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