A hockey puck raft made of lead (density= 11,300kg/m^3) with diameter 13.5cm and

Question

A hockey puck raft made of lead (density= 11,300kg/m^3) with diameter 13.5cm and height 4.0cm. A 4.0cm x 4.0cm x 4.0cm cube of Iridium (density= 22,560 kg/m^3) is suspended by a string from the bottom of lead puck. The puck and cube are then placed in a tank of mercury (density= 13,600 kg/m^3) where they are at rest and a float.

a) what is the tension in the string supporting the Iridium cube?

b) how much of the lead pucks 4.0cm height is submerged in the mercury? (note: don’t forget to account for the connected cube. )

Explanation / Answer

(a)

Net force on Iridium cube is zero

64 x 10-6 x 9.8 x 22560 = T + 64 x 10-6 x 9.8 x 13600

T = 5.62 N

(b)

Net force on Iridium cube and Lead puck is zero

64 x 10-6 x 9.8 x 22560 + 3.14 x ( 13.5 )3 x 10-6 x 11300 x 9.8 =

64 x 10-6 x 9.8 x 13600 + 3.14 x ( 13.5 )3 x 10-6 x 13600 x 9.8 x (x / 4)

x = 3.62 cm

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