To prevent the computer from shutting down after a period of non-use, you want to adjust the Energy settings, which you can typically get to by right-clicking on any blank portion of the desktop and choosing the Properties option. Then, click on the Screen Saver tab, and then choose the Power button down below. You should see settings for both your monitor and hard disk, and there should be another tab called “Hibernate” which will tell your computer whether it should just shut down entirely. Disabling hibernation should fix this.

The big problem here is that if you’re using a public machine, you may not have permission to change any of these settings. The other question is why you’re trying to defeat this on a public computer, if you’re not using it for a half hour at a time — if the library is on a budget, sending their computers to sleep when they’re not in use is a good way for them to save some money.