An iPad 2 battery contains about 90 kilojoules of energy. This is equivalent to about 20g of TNT, which is only 1/3 of the TNT used in a WWII-era "pineapple" hand grenade.
However, the real reason one can bring a laptop battery on a plane is because no terrorist has tried to use it yet. They would probably need multiple batteries: after the "shoe bomber" attack, the government determined that as little as 50g of PETN could bring down a plane, which is equivalent to 80+g of TNT, which is four iPad 2 batteries.
Even then, it would be necessary to deliver that energy in a very small amount of time, which may not be possible rapidly enough with lithium-ion; they can burn, but can they explode quickly enough, with all of their energy? The TSA aays they have studied the issue, and the answer is no [1], they "cannot be used as an explosive and are not a security threat in personal carry-on quantities."
Given that the TSA allows common lighters and matches to be taken on board, apparently not. I think aircraft cabins are designed to be "fire resistant" (for obvious reasons) though I'd be surprised if they were fireproof.
However, the real reason one can bring a laptop battery on a plane is because no terrorist has tried to use it yet. They would probably need multiple batteries: after the "shoe bomber" attack, the government determined that as little as 50g of PETN could bring down a plane, which is equivalent to 80+g of TNT, which is four iPad 2 batteries.
Even then, it would be necessary to deliver that energy in a very small amount of time, which may not be possible rapidly enough with lithium-ion; they can burn, but can they explode quickly enough, with all of their energy? The TSA aays they have studied the issue, and the answer is no [1], they "cannot be used as an explosive and are not a security threat in personal carry-on quantities."
[1] http://usatoday30.usatoday.com/money/industries/travel/2010-...