**Contest Information**

This is the current Steam Marines contest where the top 3 winners can earn Steam Marines keys redeemable via Humble (code also grants Steam/Desura keys once activated!) Rules for this contest:

- You must email your answer, with work, to yjseow@worthlessbums.com.
- Your work must be correct or close enough that I feel you've suffered enough.
- Limit two attempts per person per contest.
- Deadline is enforced based on when I receive the email.
- Winners are chosen based on speed, correctness, and general awesomeness.

**Current Contest**

The culinary officer is making delightful relativistic cookies with macadamia nuts, cranberries, and white chocolate chips. And some without the nuts for marines with nut allergies. Each little pile of cookie dough moves on a conveyor belt at speed ** S**.

A circular stamp cutter of diameter ** D** presses down on each cookie as it passes by. What shape will each cookie be in?

**(Contest ends 15 May 2014.)**

**(No in-game knowledge of Steam Marines is required to solve this problem!)**(Hint: Consider the frame of the cutter and the dough!)

**Solution**

The cutter does not strike the cookie dough simultaneously in the dough frame. In the frame of the cutter the dough is length contracted. Therefore the diameter of the cutter ** D** relates to how stretched the cookies will be.

In the dough frame the front of the cutter is ** D**v/(c

^{2}) ahead of the rear of the cutter. Because the cutter strikes the dough simultaneously in the cutter frame, time dilation makes this take y(

**v/(c**

*D*^{2})) in the dough frame (where y is the Lorentz factor.)

Because of the length contraction the front of the cutter was (initially) at a distance of y** D** from the rear of the cutter. So to solve for how stretched the cookies will be:

**/y + (y**

*D***v)/(c**

*D*^{2})

Stretch factor = y

**(1/(y**

*D*^{2}) + (v

^{2})/(c

^{2}))

Stretch factor = y

**((1 - (v**

*D*^{2})/(c

^{2})) + v

^{2})/(c

^{2}))

Stretch factor = y

*D*
So each cookie is in the shape of an ellipse with an eccentricity of v/c (simply make sure the magnitude of v is the speed ** S**.)