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 5850km on a side and 35km deep, and that the rock has an average mass density of 2750kg/m^3. The continent is moving at the rate of about 3.2cm/year.

What is the kinetic energy of the continent? Answer in the units of J.
A) 4.64 × 10^20 J
B) 4.64 × 10^24 J
C) 4.64 × 10^26 J
D) 4.64 × 10^28 J

Answer 1

The kinetic energy of the North American continent moving at a rate of 3.2cm/year can be calculated using the formula Kinetic Energy = (1/2) * mass * velocity^2. After calculating the mass of the continent and plugging in the given velocity, the answer is A) 4.64 × 10^20 J.

Step-by-step explanation:

To calculate the kinetic energy of the continent, we can use the formula:

Kinetic Energy = (1/2) * mass * velocity^2

First, we need to calculate the mass of the continent. We can find the volume using the given dimensions:

Volume = length * width * height = (5850km * 1000m/km)^2 * 35km * 1000m/km = 5850^2 * 35 * 10^9 m^3

Next, we can multiply the volume by the density to find the mass:

Mass = Volume * Density = 5850^2 * 35 * 10^9 m^3 * 2750 kg/m^3 = (5850^2 * 35 * 2750) * 10^9 kg

Finally, we can calculate the kinetic energy using the given velocity:

Kinetic Energy = (1/2) * Mass * Velocity^2 = (1/2) * (5850^2 * 35 * 2750) * 10^9 kg * (3.2cm/year * 1m/100cm * 1year/365days * 1day/24hours * 1hour/3600s)^2

Calculating this expression gives us the answer: A) 4.64 × 10^20 J.