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 35 km deep and that the rock
has an average mass density of 2700 kg/m².
The continent is moving at the rate of about
3.8 cm/year.
What is the mass of the continent?
Answer in units of kg.

Answer 1

Answer:

pt 1: $m=1.66698*10^{21} kg$

Pt 2: $KE=1212.23531 J$

Explanation:

Information Given: (p = density)

l = 5200km  d = 35km p = 2700kg/$m^{2}$

Part 1: Mass

• Find volume

1. $V=(l)^2(d)$
2. $V=(4.2*10^6)^2(35*10^3)$
3. $V=61.74*10^{16}$

• Find Mass

1. $m=Vp$
2. $m=(61.74*10^{16})(2700)$
3. $m=1.66698*10^{21}$

Part 2: Kinetic Energy

1. $v=\frac{3.8cm}{yr}*\frac{m}{100cm}*\frac{yr}{365d}*\frac{d}{24hr}*\frac{hr}{3600s}$
2. $v=1.20497*10^{-9}$

$KE=\frac{1}{2}mv^2$

$KE=\frac{1}{2} (1.66698*10^{21})(1.20497*10^{-9})^2$

$KE=1212.23531 J$

Part 3: Jogger Speed

set up, because I don't have the mass :(

Information given:

$KE_{jogger}$

1. $KE=\frac{1}{2}mv^2$
2. $v_{jogger} =\sqrt{\frac{2KE}{m_{jogger} } }$

• Input the values

Hope it helps :)