### Calculate and convert volumes

V=4/3 π r^{3}

V = 4/3 * 3.1416 * (1/2 * 8.59 in)^{3} =

4/3 * 3.1416 * 79.23 in^{3}

=331.9 in^{3}

Unity Factor: 2.54 cm = 1 in

331.9 in^{3} x (2.54 cm / 1 in)^{3} Note!!!

331.9 in^{3} x 16.39cm^{3}/in^{3}

= 5439 cm^{3}

## Mass vs. Weight

What is the mass of hydrogen?

Density of hydrogen at room temperature and 1 Atm = 0.082 g/L

What is the volume in L, assuming same size as bowling ball? Unity Factors?

1 cm^{3} = 1 mL = 10^{-3}L (Note: 1 mL = 1 cm^{3} = “1 cc”)

V (L) = 5500 cm^{3} x (1 L / 1000 cm^{3})

m (g) = V (L) * D (g/L) = 5.500 L x 0.082 g/cm^{3}

= 0.451 g

Why does the Hydrogen balloon float? F = W = m g

F = W = (0.451 g x 1 kg /1000g) * 9.8 m*s^{-2} =

= 0. 0044 N

Force Upward: (Archimedes)

D of air = 1.2 g /L; Archimedes Principle: buoyancy = mass of air displaced (6.6 g)

F = m g

F = ( 6.6 g x 1 kg /1000g) * 9.8 m*s^{-2} =

= 0. 065 N

Net force = 0.065 N - 0.044 N upwards.