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 4350 km on a side and 40 km deep, and that the rock has an average mass density of 2690 kg/m³. The continent is moving at a rate of about 4.8 cm/year. What is the mass of the continent?

Answer 1

To calculate the mass of the North American continent based on its dimensions and mass density, convert dimensions to meters, calculate the volume, and then multiply by the density. The mass is found to be 2.03 × 1021 kg.

Step-by-step explanation:

To calculate the mass of the North American continent represented by a slab of rock, given that it is 4350 km on a side and 40 km deep, with an average mass density of 2690 kg/m³, we will use the formula for the mass of a rectangular prism:

Mass = volume × density

First, we need to convert the dimensions of the slab from kilometers to meters to use the density in kg/m³:

• 4350 km × 1000 = 4,350,000 m
• 40 km × 1000 = 40,000 m

Next, we calculate the volume:

Volume = length × width × height = 4,350,000 m × 4,350,000 m × 40,000 m

Volume = 7.56 × 1017 m³

Finally, we use the density to find the mass:

Mass = 7.56 × 1017 m³ × 2690 kg/m³

Mass = 2.03 × 1021 kg

The mass of the continent is therefore 2.03 × 1021 kg.