Question

Aerogel or "solid smoke" is a novel material that is made of silicon dioxide, like glass, but is a thousand times less dense than glass
because it is extremely porous. Material scientists at NASA's Jet Propulsion Laboratory created the lightest aerogel ever in 2002, with
a density of 0.00011 pounds per cubic inch. The material was used for thermal insulation in the 2003 Mars Exploration Rover. If the
maximum space for insulation in the spacecraft's hull was 2921 cm", what mass (in grams) did the aerogel insulation add to the
spacecraft?

Answer 1

The mass that the aerogel insulation added to the aircraft, with respect to glass, is 8.8 × 10³  g.

The density of the aerogel is 0.00011 lb/in³. We will convert it to g/cm³ using the following conversion factors:

• 1 lb = 454 g

• 1 in³ = 16.4 cm³

$\frac{0.00011lb}{in^{3} } \times \frac{454g}{1lb} \times \frac{1in^{3} }{16.4cm^{3} } = 0.0030 g/cm^{3}$

If the maximum space for insulation in the spacecraft's hull was 2921 cm³, the mass that would occupy the aerogel with a density of 0.0030 g/cm³ is:

$2921 cm^{3} \times \frac{0.0030g}{cm^{3} } = 8.8 g$

Glass is about 1000 times denser than aerogel. That is,

$0.0030 g/cm^{3} \times 1000 = 3.0 g/cm^{3}$

If the maximum space for insulation in the spacecraft's hull was 2921 cm³, the mass that would occupy the glass with a density of 3.0 g/cm³ is:

$2921 cm^{3} \times \frac{3.0g}{cm^{3} } = 8.8 \times 10^{3} g$

The mass that would add the aerogel with respect to the glass is:

$8.8 \times 10^{3} g - 8.8 g \approx 8.8 \times 10^{3} g$

The mass that the aerogel insulation added to the aircraft, with respect to glass, is 8.8 × 10³  g.

You can learn more about density here: brainly.com/question/18320053