Okay, so I have a pannier on my new (used) bike (that is what the rack thing is, right?...)

So anyway I tried carrying some books strapped down with a bungee cord on it today from the library and my bungee ended up loosening itself and getting busted in my wheel. In a seperate incident, my books fell off but my bungee stayed on?

Is there something I should be using with this? What do you guys use?