Question

The current theory of the structure of the Earth, called plate tectonics, tells us that the continents are in constant motion. Assume that the North American continent can be represented by a slab of rock 5200 km on a side and 39 km deep and that the rock has an average mass density of 2820 kg/m^3. The continent is moving at the rate of about 2.2 cm/year. What is the mass of the continent? Answer in units of kg.

Answer 1

Let's first find the volume of the slab of rock:

$$V=a\cdot b\cdot c,$$

here, $a=b=5.2\cdot 10^6\ m$ is the sides of the slab of rock, $c=3.9\cdot 10^4\ m$ is the deep of the slab of rock.

Then, we get:

$$V=(5.2\cdot 10^6\ m)^2\cdot 3.9\cdot 10^4\ m=1.054\cdot 10^{18}\ m^3.$$

Finally, we can find the mass of the continent from the formula:

$$\rho=\dfrac{m}{V},$$ $$m=\rho V=2820\ \dfrac{kg}{m^3}\cdot 1.054\cdot 10^{18}\ m^3=2.97\cdot 10^{21}\ kg.$$

Answer:

$m=2.97\cdot 10^{21}\ kg.$