Question

004 (part 1 of 3) 10.0 points

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 4000 km on a side and 38 km deep and that the rock has an average mass density of 2880 kg/m3. The continent is moving at the rate of about 2.4 cm/year.
What is the mass of the continent? Answer in units of kg.
005 (part 2 of 3) 10.0 points
What is the kinetic energy of the continent? Answer in units of J.
006 (part 3 of 3) 10.0 points
A jogger (of mass 65 kg) has the same kinetic energy as that of the continent.
What would his speed be? Answer in units of m/s.

Answer 1

The mass of the represented North American continent is 1.75 x 10^15 kg. The continental slab's kinetic energy is 5.008 x 10^6 Joules. A jogger with the same kinetic energy would be running at a speed of 5.57 m/s.

Step-by-step explanation:

To calculate the mass of the continent, we use the formula: mass = volume x density. The volume of the North American continent slab represented here is the product of its length, width, and depth (4000 km x 4000 km x 38 km = 6.08 x 1011 cubic meters, since 1 km = 1000 m). With a density of 2880 kg/m3, the mass is 6.08 x 1011 m3 x 2880 kg/m3 = 1.75 x 1015 kg.

The kinetic energy of the continent is calculated using the formula: KE = 0.5 x mass x velocity2. The velocity must be in meters per second, so we convert 2.4 cm/year to m/s (2.4 cm/year x 1 year/3.156 x 107 s = 7.60 x 10-10 m/s).

Therefore, KE = 0.5 x 1.75 x 1015 kg x (7.60 x 10-10 m/s)2

= 5.008 x 106 Joules.

Assuming a jogger with a mass of 65 kg has the same kinetic energy, to find his speed, we rearrange the kinetic energy formula to solve for velocity: velocity = sqrt(2 x KE / mass).

Plugging in the values, we get velocity = sqrt(2 x 5.008 x 106 J / 65 kg) = 5.57 m/s.