5. A large OPEN tank of water is full and has a depth of 10.0 m. What is the pre

Question

5. A large OPEN tank of water is full and has a depth of 10.0 m. What is the pressure at the bottom of the tank? What would the velocity of the water be if the tank was opened at the bottom?

6. A Two balloons of identical volume (radius 11.5 m) are filled with gas. The first with helium, the second with hydrogen (H2) gas. Each balloon and cage have a mass of 750 kg. What is the lift created by each one? Which one lifts better? Remember Lift = Buoyant force - total weight. Do not forget there is weight of gas AND cage when you calculate each case.

7. A irregular piece of metal has a dry mass of 5.7 kg. Once it is submerged it has an apparent mass of 2.4 kg. What is the density of the piece of metal? See supplement folder for help on specific gravity.

8. If water leaves a tank of water at a velocity of 16.7 m/s, how tall is the tank?

Explanation / Answer

1)

a)

P = pgh

P = 1000 kg/m^2 x 9.81 m/s^2 x 10 m

P = 98100 N/m^2

b)

V = sqrt(2gh)

V = sqrt(2 x 9.81 x 10)

V = 14 m/s

2)

Assuming the balloon is a perfectly round sphere, the volume of each sphere would be

(4/3)*PI*r^3 = 6371 m^3

Density of helium = 0.1787 kg/m^3

Density of hydrogen = 0.08988 kg/m^3

Density of air =1.293 kg/m^3 (at 0 degree)

1.293 - 0.1787 = 1.1143 kg/m^3 = difference in density between air and helium

1.293 - 0.8988 = 0.3942 kg/m^3 = difference in density between air and hydrogen

6371 x 1.1143 = 7099 kg = difference in mass that the balloon would have had if filled with air instead of helium

6371 x 0.3942=2511 kg = difference in mass that the balloon would have had if filled with air instead of hydrogen

Force it takes to accelerate the mass = gravitational acceleration*mass

F = 9.81 x 7099 = 69643N = 69.6 kN for helium

F = 9.81 x 2511 = 24637N = 24.6 kN for hydrogen

So helium lifts better.

gravitational force = 9.81 x 750 = 7357.5N = 7.4kN

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