# Tunnel drilled through the Earth and mechanical work

## 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$$R_{E}$$ from the centre of the Earth, where the $$R_{E}$$ 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

$$F=-GmM_{E}d/R_{E}^3$$, 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]

$$G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}$$
$$M_{E}\ =\ 5.98\ \times\ 10^{24}\ kg$$
$$R_{E}\ =\ 6.38\ \times\ 10^{6}\ m$$
$$m\ =\ 1.0 kg$$

I get $$W\ =\ 1.1258\ \times\ 10^{7}\ J$$

According to book $$W$$ should be $$5.1\ \times\ 10^{7}\ J$$

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

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berkeman
Mentor

## 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$$R_{E}$$ from the centre of the Earth, where the $$R_{E}$$ 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

$$F=-GmM_{E}d/R_{E}^3$$, 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]

$$G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}$$
$$M_{E}\ =\ 5.98\ \times\ 10^{24}\ kg$$
$$R_{E}\ =\ 6.38\ \times\ 10^{6}\ m$$
$$m\ =\ 1.0 kg$$

I get $$W\ =\ 1.1258\ \times\ 10^{7}\ J$$

According to book $$W$$ should be $$5.1\ \times\ 10^{7}\ J$$

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