A piece of space rock weighs 20N on a scale when in air, but 15N when fully imme

Question

A piece of space rock weighs 20N on a scale when in air, but 15N when fully immersed in water of density 1300kg/m^3, What is the density of the Spacerock in kg/m^3? 2. Water is flowing in a straight horizontal pipe of variable cross section. Where the cross-sectional area of the pipe at point A is 1.70-10^-2 m^2, the pressure is 7.70-10^5 Pa and the velocity is 0.110 m/s. a) In a constricted region B, the area is 15.90middot10^-4 m^2, what is the velocity? b) What is the pressure at B (in Pa)? (Assume an ideal fluid) c) What is the volume of water passing through point A in 10 minutes d) What is the flow rate of the water in this whole pipe

Explanation / Answer

1)
W = m*g = 20 N
When in Water, W = 15 N
Density of Water , p = 1000 Kg/m^3

m*g - Fb = 15 N
20 - Fb = 15
Fb = 5 N

Fb = Density of water * Volume of object * g
5 = 1000 * Volume of object * g
Volume of object = 5/(1000*9.8)

Density of object = Mass/Volume
Density of object = (20/g) / 5/(1000*g)
Density of object = 4000 Kg/m^3

(2)
A1 = 1.7 * 10^-2 m^2
Pa = 7.7 * 10^5 Pa
V1 = 0.110 m/s

(a)
A2 = 15.90 * 10^-4 m^2

Using Continuity eq,
A1*V1 = A2*V2
1.7 * 10^-2 * 0.110 = 15.90 * 10^-4 * V2
V2 = 1.176 m/s

Using Bernoulli Theorem,
Pa + ½*v12 = Pb + ½v22
7.7 * 10^5 + 1/2 * 1000 * 0.110^2 = pb + 1/2 * 1000 * 1.176^2
pb = 7.69 * 10^5 Pa

Volume of water flowing through A in 10 min,
V = A1*V1*t
V = 1.7 * 10^-2 * 0.110 * 10 * 60 m^3
V = 1.122 m^3

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