In general 'sudo' in a cron script is a bad idea. Also, in your scripts are you using the full path/command? You should do that. Are you cable to just install the job under root?
The jist of it is it uses the sudo command to change the permissions of a file, making it writable, then empties the contents of said file (cat > /dev/null).
So without the sudo command, the file cannot be emptied.