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 can be represented by a slab of rock 4000km on a side and 33 km deep and that the rock has an average mass density of 2690 kg/m^3. The continent is moving at the rate of about 2.4 cm/year. a.) What is the mass of the continent?

b.) What is the kinetic energy of the continent?

c.) A jogger (of mass 75 kg) has the same kinetic energy as that of the continent. What would his speed be?

a) m = 1.42*10²¹ [kg]

b) Ek = 411.21 [J]

c) v = 3.31 [m/s]

Explanation:

In order to solve this problem, we must find the mass of the continent using the definition of density which tells us that it is equal to the mass over the volume.

a)

Ro = density = 2690 [kg/m³]

Ro = m/V

where:

m = mass [kg]

V = volume [m³]

The side of the slab is 4000 [km] = 4000000 [m]

and the deep is 33 [km] = 33000 [m]

Therefore the volume is equal to:

V = (4000000² * 33000)

V = 5.28*10¹⁷ [m³]

Now we can find the mass.

m = Ro*V

m = 2690*5.28*10¹⁷

m = 1.42*10²¹ [kg]

b)

The kinetic energy can be calculated by means of the following expression.

Ek = 0.5*m*(v²)

But first we must convert the velocity from [cm/year] to [m/s]

v = velocity = 2.4[cm/year]*1[m/100cm]*1[year/365day]*1[day/24h]*1[h/3600s]

v = 7.61*10⁻¹⁰[m/s]

Ek = 0.5*(1.42*10²¹ )*(7.61*10⁻¹⁰)²

Ek = 411.21 [J]

c)

We use the same equation to find the velocity.

Ek = 0.5*m*(v²)

411.21 = 0.5*75*v²

v² = 10.965 (we use the rootsquare)

v = 3.31 [m/s]