My computer keeps randomly shutting off and I don't know why, help?

I've noticed this problem with other computers, but haven't been able to get it fixed and haven't been able to figure out why. Anyway, my computer sometimes randomly shuts off, and I can hear the fan completely shut down. This happens randomly it seems, I could be typing something, or my sister could slam the table and at first I thought some vibration made it shut down or something. But it's also happened before, when bringing my computer places.

And when it shuts off, occasionally, it doesn't turn on for a few minutes, hours and once didn't turn on for a few days. And when it finally does turn on, it either restarts, or shows up this faded screen of what I was last doing on my computer with a loading bar at the bottom.

It's been happening more frequently lately and I dont' know why. My sister has the same model and same age Macbook same type of battery, and it doesn't happen to her. I've gone to the support forums and tried everything.

Anyone know what's going on?