Density

Problems

practice

  1. Your Mother gives you a kilogram of aluminum and a kilogram of lead. Both objects are solid, rectangular blocks.
    1. Which is more massive on the surface of the earth?
    2. Which is more massive on the surface of the moon?
    3. Which is heavier on the surface of the earth?
    4. Which is heavier on the surface of the moon?
    We will return to this question in the section on buoyancy.
  2. A lucite cube has a mass of 142.5 g and a width of 4.9 cm. Determine its density in kg/m3.
       
    Lucite Cube on Electronic Balance Ruler Next to Lucite Cube
       
  3. It has been known for several thousand years that the earth is spherical (by educated people, at least). Sometime in the Second Century BCE the size of the earth was determined (rearth = 6,370 km). By the Nineteenth Century its mass was known (mearth = 5.97 × 1024 kg). And in the early Twentieth 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.
     
    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 …
    1. the average density of the entire earth
    2. the percent of the earth's mass located in the mantle, and
    3. the average density of the core.
  4. Write something completely different.

conceptual

  1. 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 mayonnaise heavier than traditional mayonnaise?
  2. Why does "heavy cream" have a lower density than "light cream"? Explain this apparent contradiction.

numerical

  1. 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.
  2. 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  
     
     
  3. Complete the following table with values in SI units.
     
    object mass (kg) radius (m) density (kg/m3)
    iron shot put 7.26
    (16 lbs)
    iron atom
    (55.847 u)
    iron atom's
    electron cloud
    (26 melectron)
    iron nucleus
    (55.847 u)
    (~4 fm)
     

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