Your mother gives you a kilogram of aluminum and a kilogram of lead. Both objects are solid, rectangular blocks.
Which is more massive on the surface of the Earth?
Which is more massive on the surface of the moon?
Which is heavier on the surface of the Earth?
Which is heavier on the surface of the moon?
Special notes:
The phrase "more massive" should be read literally as "has more mass" not "fills more space".
The phrase "heavier" should be read as "is pulled down more strongly by gravity" not "is more dense".
A variation on this practice problem appears later in the section on buoyancy.
A lucite cube has a mass of 142.5 g and a width of 4.9 cm. Determine its density in kg/m3.
It has been known for several thousand years that the Earth is spherical (by educated people, at least). Sometime in the 2nd century BCE the size of the Earth was determined (r♁ = 6,370 km). By the 19th century its mass was known (m♁ = 5.97 × 1024 kg). And in the early 20th century the structure of the Earth was deduced. The Earth has three main layers: crust, mantle, and core. The crust of the is the lightest and thinnest and, like the shell of an egg, contributes little to its overall mass. The mantle is a bit more dense, substantially thicker, and contains most of the Earth's mass. The core is the densest layer (but not the most massive) and is divided into a liquid outer core and a solid inner core. The relevant data for the interior of the Earth are summarized below.
The structure of the Earth
layer
depth range (km)
mean density (kg/m3)
consistency
crust
0 ~ 20
2700
solid
mantle
20 ~ 2890
4500
plastic
outer core
2890 ~ 5160
?
liquid
inner core
5160 ~ 6370
?
solid
Determine…
the average density of the entire Earth
the percent of the Earth's mass located in the mantle, and
the average density of the core.
Write something completely different.
conceptual
Mayonnaise is essentially a mixture of vegetable oil and water with a bit of egg yolk added as an emulsifier (a substance that keeps the oil and water from separating). Traditional mayonnaise has a density of about 910 kg/m3 while reduced fat, low calorie, or "light" mayonnaise has a density of about 1000 kg/m3. Why is "light" (low calorie) mayonnaise "heavier" (more dense) than traditional mayonnaise?
Why does "heavy cream" have a lower density than "light cream"? Explain this apparent contradiction.
numerical
Find the mass of the air contained in a room that is 16.40 m long by 4.5 m wide by 3.26 m high.
How much larger is a 152.8 g tomato at room temperature (20 °C) than when it is in a really cold refrigerator (4 °C)? Assume tomatoes are spheres of pure water. Give your answer in cubic centimeters or milliliters, your choice. (That's a joke by the way. Milliliters and cubic centimeters are identical. Also, I realize that tomatoes are not actually spheres of pure water. Physicists approach problems by approximation. Let's not make this problem any more difficult than it needs to be. A tomato is a sphere of pure water for now. Also, I realize that tomatoes lose flavor when chilled. Avoid putting fresh tomatoes in the refrigerator.)
statistical
Determine the mean density of the Earth, moon, and sun. (That's the mean value for each object individually, not the mean of all three objects collectively.) Compile your results in a table like the one below.
object
mass
radius
density (kg/m3)
the Earth
the moon
the sun
Determine the density of the following astronomical objects arranged in order of increasing mass. (Pay attention to the units.)
object
mass
radius
density (kg/m3)
the sun
1.99 × 1030 kg
696,000 km
white dwarf star
0.5 to 1.4 solar masses
5000 km
neutron star
1.4 to 3 solar masses
10 km
stellar black hole
more than 3 solar masses
2Gm/c2 (event horizon)
supermassive black hole
> 106 solar masses
2Gm/c2 (event horizon)
the known universe
1053 kg
13.8 × 109 light years
It is usually said that the moon has no atmosphere, but this is not quite true. The moon's atmosphere is nowhere near as dense as the Earth's or even that of Mars (which is pretty thin) but it is more dense than the "vacuum" of interplanetary space. The table below gives the partial densities of the constituent gases in the moon's atmosphere in particles per cubic centimeter.
