Please show all work. Please verify that your answer is correct. Thank you!! 5.

Question

Please show all work. Please verify that your answer is correct. Thank you!!

5. A large 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?

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?

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

Explanation / Answer

5.

The two formulas you will need to use are:

P = pgh {density * gravity * height}
V = sqrt(2gh) {2 * gravity * height}

Substituting the information you get

Part one:
P = (1000 kg/m^2) ( 9.8 m/s) * (10m) = 9.8 X 10^4 (98000) N/m^2

Part two:
V = sqrt(2 * (9.8m/s) * (10m)) = 14 m/s

6.

Assuming the balloon is a perfectly round sphere, the volume of each sphere would be (4/3)*PI*r^3=6371m^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*1,1143=7099 kg =difference in mass that the balloon would have had if filled with air instead of helium
6371*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*7099=69643N=69,6 kN for helium
F=9,81*2511=24637N=24,6 kN for hydrogen

So helium lifts better.
gravitational force=9,81*750=7357,5N=7,4kN

F=69,6-7,4=62,3kN= total lifting force helium
F=24,6-7,4=17,3kN= total lifting force hydrogen

7.

You need the density of the liquid it was submerged into. When submerged, the metal lost 3.3 kg. Let's say it was submerged into water, which has the density of 1000 kg/m3. An object loses the same amount of weight that the liquid it pushed out has. So it pushed out 3.3 kg of water, it also pushed out 0.0033 m3 of water. That means that is its volume. And the formula for density is mass divided by volume so 5.7/0.0033 = 1727.27. The density of metal is 1727.27 kg/m3 or 1,727 g/cm3. That's in case of water. If it's any other liquid, to simplify, the formula is:
change in mass of the submerged metal in kg (3.3) divided with the density of liquid in kg/m3. That gives you volume of the metal. Then divide the original mass of the metal (5.7) with that volume. And you get the density of the metal.
Pretty simple, hope you understood.

8.

You can solve this with Bernoulli's principle, or if you haven't learned that yet, conservation of energy:
PE(top) = KE(bottom)
mgh = 1/2 mv^2
h = v^2 / 2g

h = (16.7 m/s)^2 / (2*9.8 m/s^2)
h = 14.2 meters

Edit:
Made a calculator error earlier, correct answer is 14.2 meters.

Correction to answer below:
Using Bernoulli's principle, one can show that the velocity of the jet is independent of the size of the hole.

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