I assume the picture is not a stock photo but shows your camera with the mirror stuck up and the shutter stuck open.

Then you have one of two versions of the “old” F-1. I can't tell from the picture whether it's the very first model or the “F-1 (later model)” – commonly referred to as F-1n. Both, “F-1” and “F-1 (later model)” have all mechanically controlled shutter speeds and the battery is only needed for the meter. It's not essential for this issue but you can tell them apart by their maximum film speed setting as Corey has outlined above.

You don't have a “New F-1” which has a different front layout (e.g. no self-timer, different stop-down lever). The “New F-1” has shutter speeds of 1/60s and slower controlled electronically.

This problem does not occur due to the battery being dead.

If it is the slow speeds (60, 30, 15 ...) which are affected, a dirty escapement could be the culprit. This is not an uncommon issue with the F-1. But this is not something you can fix at home. Have the camera checked by someone who knows how to service mechanical cameras. If you are lucky it just needs a CLA (clean, lube, adjust).