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## Homework Statement

Suppose that a straight tunnel is drilled through the Earth as indicated in figure. Assume that the floor of the tunnel is frictionless and that air resistance can be neglected. If the mid-point of the tunnel is 0.8[tex]R_{E}[/tex] from the centre of the Earth, where the [tex]R_{E}[/tex] is the radius of the Earth, determine the mechanical work done by the field force in moving a 1.0 kg mass from the entrance of the tunnel to the mid-point.

## Homework Equations

[tex]F=-GmM_{E}d/R_{E}^3[/tex], where the d is distance from the centre of the Earth

## The Attempt at a Solution

http://img35.imageshack.us/img35/323/soltry.jpg [Broken]

[tex]G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}[/tex]

[tex]M_{E}\ =\ 5.98\ \times\ 10^{24}\ kg[/tex]

[tex]R_{E}\ =\ 6.38\ \times\ 10^{6}\ m[/tex]

[tex]m\ =\ 1.0 kg[/tex]

I get [tex]W\ =\ 1.1258\ \times\ 10^{7}\ J[/tex]

According to book [tex]W[/tex] should be [tex]5.1\ \times\ 10^{7}\ J[/tex]

What did I do wrong? Or is the answer in the book wrong?

Thank you for in advance!

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