okay, for this, you would need to specify in the /etc/fstab file what permissions you want /mnt/floppy to have. you do this by setting a number of flags (is that the right term? they are options anyway) to tell the system what permissions to give that directory at the time when it mounts it.
To see what your current fstab file looks like, type 'less /etc/fstab' and to change it, you will need to be root and edit /etc/fstab with some text editor. i'd use pico or emacs myself, but whatever you are familiar with.
To find out what options you can specify, do 'man mount' and i think there is probably a 'man fstab' as well.
Specifying the 'umask' value is directly related to your chmod numbers. The difference is that the numver you put after umask is what you take away from 777 to get the actual permission number (christ i am explaining this in all the wrong words!) so if you put umask as 000, it would mean permissions of 777, and if you put umask as 012, it would mean permissions of 765.
somebody else will come along no doubt and answer in more specific terms, but that's the gist.
here's a good startoff page about this subject but now you know what to look for, go and google it for more specific answers.
I hope what i said was helpful, i am in a bit of a dithery mood today but i tried to be as useful as i could!