Concept explainers
Assume that the earth is a solid sphere of uniform density with mass M and radius R = 3960 mi. For a particle of mass m within the earth at a distance r from the earth’s center, the gravitational force attracting the particle to the center is
(a) Show that
(b) Suppose a hole is drilled through the earth along a diameter. Show that if a particle of mass m is dropped from rest at the surface, into the hole, then the distance y = y(t) of the particle from the center of the earth at time t is given by y"(t) = -k2y(t)
where k2 = GM/R3 = g/R.
(c) Conclude from part (b) that the particle undergoes simple harmonic motion. Find the period T.
(d) With what speed does the particle pass through the center of the earth?
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Chapter 17 Solutions
Multivariable Calculus
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