Question

1. If water leaves a tank of water at a velocity of 16.7 m/s, how tall is the tank? 2. 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? 3. 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? Please show your work

Answer 1

Answer 1

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

answer 2

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 (=5.7-2.4) 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.

Answer 3

The balloons are 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