A) We need to first determine the volume of the continent and then mass would be = Volume x density
Volume = 4.7 x 10^6 m x 4.7 x 10^6 m x 37 x 10^3m
= 817 x 10^15 cubic meter
Mass = V x density
= 817 x 10^15 cubic meter x 2720kg/m^3
= 2.2 x 10^21 Kg
B)
Kinetic Energy = ½mV²
= ½ x 2.2 x 10^21 Kg x ( 4.6cm/year. x 1m/100cm x 1yr/365.24day x 1day/24hr x 1hr/3600s)²
= 2340 J
Answer:
(A) Volume of the rock is [tex]817\times10^{15}\;\rm{m^3[/tex]
(B) Kinetic energy of the continent is [tex]2340\;\rm{J[/tex]
Explanation:
Given: The North American continent can be represented by a slab of rock [tex]4700\;\rm{km[/tex] on a side and [tex]37\;\rm{km[/tex] deep and that the rock has an average mass density of [tex]2720\;\rm{kg/m^3[/tex]. The continent is moving at the rate of about [tex]4.6\;\rm{cm/year[/tex].
As mentioned in question,
[tex]\rm{mass=volume\times\;density[/tex]
(A) Volume of the rock is calculated as
[tex]V=4.7\times10^6\times4.7\times10^6\times37\times10^3\\V=817\times10^{15}\;\rm{m^3}[/tex]
Now, [tex]\rm{mass}=817\times10^{15}\times2720\;\rm{kg\\\rm{mass}=2.2\times10^21\;\rm{kg[/tex]
(B) kinetic energy of the continent is calculated as[tex]K.E=\frac{1}{2}mv^2\\K.E=\frac{1}{2}\times2.2 \times 10^{21} \;\rm{kg} \times ( 4.6\;cm/year \times 1\;m/100\;cm \times1\;yr/365\;24\;day \times 1\;day/24\;hr \times 1\;hr/3600\;s)^2\\K.E=2340\;\rm{J[/tex]
Hence, (A) Volume of the rock is [tex]817\times10^{15}\;\rm{m^3[/tex]
(B) Kinetic energy of the continent is [tex]2340\;\rm{J[/tex].
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