# Test Prep for AP® Courses

### 11.2 Density

An under-inflated volleyball is pumped full of air so that its radius increases by 10 percent. Ignoring the mass of the air inserted into the ball, what will happen to the volleyball's density?

- The density of the volleyball will increase by approximately 25 percent.
- The density of the volleyball will increase by approximately 10 percent.
- The density of the volleyball will decrease by approximately 10 percent.
- The density of the volleyball will decrease by approximately 17 percent.
- The density of the volleyball will decrease by approximately 25 percent.

A piece of aluminum foil has a known surface density of 15 g/cm^{2}. If a 100-gram hollow cube were constructed using this foil, determine the approximate side length of this cube.

- 1.05 cm
- 1.10 cm
- 2.6 cm
- 6.67 cm
- 15 cm

A cube of polystyrene measuring 10 cm per side lies partially submerged in a large container of water.

- If 90 percent of the polystyrene floats above the surface of the water, what is the density of the polystyrene? Note: The density of water is 1,000 kg/m
^{3}. - A 0.5 kg mass is placed on the block of polystyrene. What percentage of the block now remains above water?
- The water is poured out of the container and replaced with ethyl alcohol (density = 790 kg/m
^{3}).- Will the block be able to remain partially submerged in this new fluid? Explain.
- Will the block be able to remain partially submerged in this new fluid with the 0.5 kg mass placed on top? Explain.

- Without using a container of water, explain how you could determine the density of the polystyrene mentioned above if the material instead were spherical.

Four spheres are hung from a variety of different springs. The table below describes the characteristics of both the spheres and the springs from which they are hung. Use this information to rank the density of each sphere from least to greatest. Show work supporting your ranking.

Material Type | Radius of Sphere | Stretch of Spring (from equilibrium) | Spring Constant |
---|---|---|---|

A | 10 cm | 5 cm | 2 N/m |

B | 5 cm | 8 cm | 8 N/m |

C | 8 cm | 10 cm | 6 N/m |

D | 8 cm | 12 cm | 10 N/m |

Rank the densities of the objects listed above, from greatest to least. Show work supporting your ranking.

### 11.3 Pressure

A cylindrical drum of radius 0.5 m is used to hold 400 liters of petroleum ether (density = .68 g/mL or 680 kg/m^{3}).

(Note: one liter = 0.001 m^{3})

- Determine the amount of pressure applied to the walls of the drum if the petroleum ether fills the drum to its top.
- Determine the amount of pressure applied to the floor of the drum if the petroleum ether fills the drum to its top.
- If the drum were redesigned to hold 800 liters of petroleum ether:
- How would the pressure on the walls change?
Would it increaase, decrease, or stay the same?

- How would the pressure on the floor change?
Would it increase, decrease, or stay the same?

- How would the pressure on the walls change?