1. Knows: Mass of Earth: `M_e = 5.97 times 10^(24) kg` Radius of Earth: `r_e = 6.37 times 10^6 m` (a) Use above information to calculate the average density of the Earth. (b) Where does the value fit among those listed in Table 14.1. Look up the density of a typical surface rock like granite in another source and compare it with the density of the Earth.
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2. An automobile company displays a die-cast model of its first car, made from 9.35 kg of iron. To celebrate its hundredth year in business, a worker will recast the model in solid gold from the original dies. What mass of gold is needed to make the new model? Given: Density of iron: `ρ_i = 7.86 times 10^3 kg//m^3` Density of gold: `ρ_g = 1.93 times 10^4 kg//m^3`
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3. Figure P1.8 shows a frustum of a cone. Match each of the expressions (a) `pi(r_1 + r_2)[h^2 + (r_2 - r_1)^2]^(1/2),` (b) `2pi(r_1 + r_2)`, and (c) `pih(r_1^2 + r_1r_2 + r_2^2)//3` with the quantity it describes: (d) the total circumference of the flat circular faces, (e) the volume, or (f) the area of the curved surface.
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4. Newton’s law of universal gravitation is represented by `F = (GMm)/ (r^2)` where `F` is the magnitude of the gravitational force exerted by one small object on another, `M` and `m` are the masses of the objects, and `r` is a distance. Force has the SI units `kgcdotm//s^2`. What are the SI units of the proportionality constant G?
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