1. Show that the density of a 5-kg solid cylinder that is 10 cm tall with a radius of 3 cm is 17.7 g/cm3.
2. What is the weight of a cubic meter of cork? Could you lift it? (For the density of cork, use 400 kg/m3.)
3. A certain spring stretches 6 cm when a load of 30 N is suspended from it. How much will the spring stretch if 50 N is suspended from it (and it doesn't reach its elastic limit)?
4. Consider a spring that stretches 4 cm when a load of 10 N is suspended from it. How much will the spring stretch if an identical spring also supports the load as shown in (a) and (b)? (Neglect the weights of the springs.)
5. A cube 2 cm on a side is cut into cubes 1 cm on a side.
a. How many cubes result?
b. What was the surface area of the original cube and what is the total surface area of the eight smaller cubes? What is the ratio of surface areas?
c. Show that the surface-to-volume ratio of the smaller cube is twice as great as for the single larger cube.
6. A 19.3-g mass of gold in the form of a cube is 1 cm long on each side (somewhat smaller than a sugar cube). What would be the length of the sides of a cube having twice this mass of gold?
7. In 2009, one of the U.S government's bailout packages was $700 billion when gold was worth $800 per ounce ($28.20 per gram). Calculate the mass in grams of $700 billion worth of gold. If this amount of gold were in the shape of a cube, how long would each of its sides be?