At 1130 you should definitely be sleepy
... Not sure what you do for a living, but most people I know are in bed by 10 - 11PM... then get up at 630-7AM... I find that on Friday I go to bed sometimes at 930, just the week getting under my skin, I figure, and I get up at 8AM... My usual time to sleep Mon to Thurs is 11PM to 630AM...
So all this to say that yes give in to the tiredness, specially at 1130pm, your body is telling you something...