Chapter 15 43) A solid block is attached to a spring scale. When the block is su

Question

Chapter 15

43) A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 20.0 N; when it is completely immersed in water, the scale reads 17.7 N. What are (a) the volume and (b) the density of the block?

44) As in the previous problem (43), a solid block is suspended from a spring scale. If the reading on the scale when the block is completely immersed in water is 25.0 N and the reading when it is completely immersed in alcohol of density 806 kg/m^3 is 25.7 N, what are (a) the block's volume and (b) density?

Explanation / Answer

(43.) Let volume of solid block be V.

Weight(in air) = 20 N = m*g = Ds*V*g N

Ds = density of the solid block.

Dw = 1000 kg/m^3 ; g = 10 m/s^2

Weight(immersed in water) = 17.7 N = Ds*V*g - Dw*V*g N

Force of buoyancy = Dw*V*g N

a.) Dw*V*g = 20 - 17.7 N = 2.3 N

V = 2.3 / (1000*10) = 2.3*10^-4 m^3

V =  2.3*10^-4 m^3

b.) Ds*V*g = 20 N

Ds = 20 / (10*2.3*10^-4 ) = 8.6956*10^3 kg/m^3

Ds = 8.6956*10^3 kg/m^3

(44.) Weight(water) = Ds*V*g - Dw*V*g = 25 N

Weight(alcohol) = Ds*V*g - Da*V*g = 25.7 N

a.) (Dw - Da)*V*g = 0.2 N

Da = 806 kg/m^3

V = 0.2 / (10*194) = 1.03092*10^-4 m^3

b.) Ds*V*g = 25 + Dw*V*g N = 25 + 1000*1.0309278*10^-4*10 = 26.03092 N

Ds = 26.03092 / (1.0309278*10^-4*10) = 2.5250184*10^4 kg/m^3

Ds =  2.5250184*10^4 kg/m^3

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