The following seemed simple enough to me . . . I'm somewhat sure about the requisite physics, but shakey on the integrals:(adsbygoogle = window.adsbygoogle || []).push({});

A particle of mass m is released from rest a distance b from a fixed origin of force that attracts a particle according to the inverse square law:

F(x) = -kx^{-2}

Show that the time required for the particle to reach the origin is:

π(mb^{3}/8k)^{1/2}

And then I reviewed the hints provided by the author -- the very first of which completely stumped me. My rusty calc skills not withstanding, how is the following hint true:

Show that dx/dt = -(2k/m)^{1/2}· (1/x - 1/b)^{1/2}

the negative sign results from the physical situation

the subsequent hint is also a mystery to me:

Show that t = sqrt(mb^{3}/2k) · ∫sqrt[y/(1-y)]dy

where y = x/b (evaluated from 1 to 0)

the 3rd hint is likewise elusive to me:

Show that setting y=sin^{2}θ results in t = sqrt(mb^{3}/2k) · ∫2sin^{2}θdθ (evaluated from π/2 to 0)

let alone the final result of π(mb^{3}/8k)

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# Deceptively Difficult Physics Integration Problem (Restorative Forces)?

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