[CentOS] Cronjob script with date stamp?

I have a cron job that calls a shell script - the script invokes dump.

I'd like to do two things:

- Have the script dump the results of the job to a text file. I tried this with /path/to/dump my switches -v >> /home/me/dump.log

But that just produced an empty file.

- Have the dump file be date-stamped with the date it was executed. Right now, I manually edit the script to change the filename to the date the dump will be taken.

To get a differential dump, would I have dump produce its output to the same file each time? I would not want to overwright the existing contents. I'm currently dumping to a file on an external hard drive, but will eventually go to tape.

Thanks for feedback.

Scott