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)

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Deceptively Difficult Physics Integration Problem (Restorative Forces)?

Loading...

Similar Threads for Deceptively Difficult Physics | Date |
---|---|

I Physics? Setting up PDE for air resistance at high velocity | Nov 25, 2017 |

General Solution of a Poisson Equation (maybe difficult) | Apr 5, 2015 |

How difficult is it to solve this elliptic ODE. | Nov 29, 2013 |

Difficult differential equation | Nov 18, 2013 |

**Physics Forums - The Fusion of Science and Community**