Review Knight\'s textbook, Chapter 13, Section 13.4 A 10cm x 10cm times 10cm blo

Question

Review Knight's textbook, Chapter 13, Section 13.4 A 10cm x 10cm times 10cm block of steel (rho_steel = 7900kg/m^3) is suspended from a spring scale. The scale is in Newtons. What is the scale reading if the block is in air? What is the scale reading after the block has been lowered into a beaker of water and is completely submerged? When analyzing a sample of ore, a geologist finds that it weighs 2.00N in air and 1.13N when immersed in water. What is the density of the ore? What assumptions did you make to answer this question?

Explanation / Answer

Q2)

Volume:

V = 1000 cm^3

   = 10^-3 m^3

(a)

Scale reading in air:

W = d V g

    = 7900 * 10^-3 * 9.8

    = 77.42 N

    = 77 N (rounded to 2 SF)

(b)

Upthrust force:

Fb = d (of water) V g

     =10^3 * 10^-3 * 9.8

    = 9.8 N

Scale reading in water:

Reading = W - Fb

              =77.42 - 9.8

              = 67.62 N

             = 68 N (rounded to 2 SF)

Q3)

Wair = 2.00 N

Wwater = 1.13 N

Assumption:

Density of water = 1000 kg/m^3

Relative density:

RD = Wair / ( Wair - Wwater )

      = 2.00 / ( 2.00 - 1.13 )

      = 2.2989

Density of the ore:

D = RD * Density of water

   = 2.2989 * 1000

   = 2298.9 kg/m^3

   = 2.30 x 10^3 kg/m^3 (rounded to 3 SF)

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