- #1

- 15

- 0

## Homework Statement

*A wire stretches from one side of an Earth-orbiting space station to the other through the centre of mass of the station, such that it always points along a radial line to the centre of the Earth. A bead is threaded on the wire and initially rests 1.0 m from the centre of mass position, on the side away from the Earth.*

Ignoring friction between the wire and bead, determine the time it takes for the bead to move 2.6 m further away from the Earth, given the space station orbits at an altitude of 216 km.

Ignoring friction between the wire and bead, determine the time it takes for the bead to move 2.6 m further away from the Earth, given the space station orbits at an altitude of 216 km.

## Homework Equations

[itex]\left |\vec{g}\right |=\frac{GM}{r^2}[/itex]

## The Attempt at a Solution

I've not managed to make any mathematical progress since I don't know how to apply the physics.

Specifically: ignoring the orbit for now, the bead wouldn't undergo SHM about the centre of mass (COM). Therefore I think that it must be a superposition of the bead attraction to the CoM and its 'centrifugal' tendency to move away from the Earth, is the equation of motion I need to set up to then solve for time. But I don't have a clue as to how to quantify centrifugal motion, given that the centripetal based Newton's II Law is not applicable here (I think at least!) ?