Chapter 35, The Earth as a Terrestrial Planet Video Solutions, Pathways to Astronomy

Problem 1

$P$ waves travel at about $6 \mathrm{km} / \mathrm{sec}.$
a. At this speed, how long would it take $P$ waves to travel to the opposite side of the Earth from the center of an earthquake?
b. In the iron core, the speed of $\mathrm{P}$ waves is approximately two times faster. Sketch a picture of the interior of the Earth and estimate how much sooner the wave would reach the opposite side of the Earth if the wave traveled this much faster while in the core.

Raj Bala

Numerade Educator

07:14

Problem 2

Draw a scale model of the Earth (radius $6357 \mathrm{km}$ ) and the liquid core (radius $3500 \mathrm{km}$ ). How large a region is "shadowed" from $S$ waves? Use a protractor to estimate how many degrees away from the site of the earthquake $S$ waves are still detected.

Victor Salazar

Numerade Educator

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Problem 3

S waves travel slower than P waves-about 4 km/sec versus $6 \mathrm{km} / \mathrm{sec} .$ Suppose a seismometer detects $\mathrm{P}$ waves at $7 ; 00 \mathrm{P.M.}$ and S waves at 7: 05 P.M. How far away was the earthquake? At what time did the earthquake occur?

Lainey Roebuck

Numerade Educator

02:27

Problem 4

Suppose the Earth were made of nothing but iron (at a density of $7.8 \mathrm{kg} / \mathrm{L}$ ) and silicates (at a density of $3.0 \mathrm{kg} / \mathrm{L}$ ).
a. Calculate the percentage (by volume) of iron and silicates that would be required to give a density of $5.5 \mathrm{kg} / \mathrm{L}$. (Hint:
you know that the two volume percentages must add up to $100 \%,$ so the percentage of silicates equals $100 \%$ minus the percentage of iron.)
b. The outer radius of the core is approximately $3500 \mathrm{km}$ while the overall radius of the Earth is $6357 \mathrm{km}$ What percentage of the Earth's volume is occupied by the core?
c. The percentage of Earth's mass that is composed of iron is estimated to be $32 \%$ (see Unit 33 ). What might explain why this percentage is smaller than the value in (a) and larger than the percentage in (b)?

Ronald Prasad

Numerade Educator

01:27

Problem 5

We can get a rough estimate of how fast the rift zone in the Atlantic Ocean is moving the continents of South America and Africa apart simply by assuming that at 240 million years ago Natal, Brazil, and Douala, Cameroon, occupied the same neighborhood. Theses cities are presently $5000 \mathrm{km}$ apart. How fast would they have to be moving, on average, to reach their present separation? Express your result in cm/year.

Kayla Day

Numerade Educator

01:19

Problem 6

In 2005 the Earth's magnetic field was about $10 \%$ weaker than it was in 1845 when German mathematician Carl Friedrich Gauss first measured it. If the magnetic field continues to weaken by $10 \%$ of its current value every 160 years approximately when will it be at half of its 1845 value? When will it be only $10 \%$ of its 1845 value? (Note that we are supposing, in this question, that after 320 years the strength of the field is $90 \%$ of $90 \%-$ or $81 \%$ of its original value.

Donya Dobbin

Numerade Educator