exposure - Does a full frame lens require more light on a crop body?

When using a full frame lens on a crop body, does the lens require more light?

If I use an f/2.8 full frame lens on a crop body, does it become an f/4.2 (*1.5)?

Answer

The amount of light passed through the lens stays the same, the lens will still be a F/2.8 lens.

Since the smaller sensor only crops out a different area from the illuminated circle, the exposure related properties of the image taking process will stay the same, regardless of the crop-factor.