(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A bead of mass m slides along the x-axis between two spheres of mass M equidistant from the x-axis (distance d) and attract the bead gravitationally.

a. Find the potential energy of the bead.

b. The bead is released at x = 3d with an initial velocity toward the origin. Find the speed at the origin.

c. Find the frequency of small oscillations of the bead about the origin.

2. Relevant equations

[tex]U = -\int F dx[/tex]

[tex]F_{grav} = \frac{-GMm}{r^2}[/tex]

[tex]E = U + K[/tex]

[tex]K = \frac{1}{2}mv^2[/tex]

3. The attempt at a solution

Integrating the force of gravity, I find that the potential energy of the force is [tex]\frac{GMm}{r^2}*{R_{M}}^2*(\frac{1}{R_{M}} - \frac{1}{r})[/tex] where [tex]r[/tex] is the distance straight from [tex]m[/tex] to one of the spheres [tex]M[/tex] and [tex]R_M[/tex] is the radius of [tex]M[/tex]. This is fine, but I'm stuck on how to set the potential in terms of d, which I will need to find the velocity in the next part.

Conceptually, I know the y component of the gravitational forces cancel out since the spheres are equal mass and distance away. Also, the potential I get for the x component will need to be doubled since there are two masses.

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# Homework Help: Potential energy of gravitational force

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