Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 10 - Fluids - Problems - Page 285: 7

Answer

See answers.

Work Step by Step

a. The density is the total mass divided by the total volume. Let subscript 1 represent the inner core, subscript 2 represent the outer core, and subscript 3 represent the mantle. The radii are the outer radii. $$V_1=\frac{4\pi}{3}r_1^3$$ $$M_1=\rho_1 V_1$$ $$V_2=\frac{4\pi}{3}(r_2^2-r_1^2)$$ $$M_2=\rho_2 V_2$$ $$V_3=\frac{4\pi}{3}(r_3^2-r_2^2)$$ $$M_3=\rho_3 V_3$$ $$\rho_{3\;layers}=\frac{M_1+M_2+M_3}{V_1+V_2+V_3}=5500\;kg/m^3$$ b. The actual density is the mass divided by the volume. $$\rho_{actual}=\frac{5.98\times10^{24}kg}{\frac{4\pi}{3}(6380000\;m)^3}\approx 5500\;kg/m^3$$ A more accurate accounting shows that the 3-layer model overestimates the actual density by about 0.07 percent.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.