Firefox won't run java apps

Since I bought my Mac a couple of weeks ago, i've not been able to run any java apps with Firefox (Safari runs java fine). Two website apps that I use frequently just won't work - both seem to have a problem with the java version. I updated to the latest version of Firefox 3.6.15 and I have the latest Java version 1.6.0_24 (previously I was on 1.6.0_11). I did notice when I first tried to run a Java app one of the websites said I need to upgrade to java 1.6.0_11 even though I was already on it. I have cleared caches on both java and firefox, and still doesn't work. In windows I could just uninstall java and reinstall it, but don't know how to do that on Mac (or if I even should, maybe there's an easy fix).

Any ideas?