When camping in a bear country, will a tent provide an additional protection from bears, as opposed to just sleeping outside or in a hammock? Provided I take the usual precautions of keeping any food, toothpaste etc in some other place than the one I sleep at?
No, a tent will not give you any protection from bears that want what's inside. If you want to use one thats fine, but don't go getting a false sense of security.
In some ways a tent could be an attractant if:
These smells can get into the fabric and stick around for a while.
There are a lot of backcountry veterans who sleep "open sky", even in winter using nothing but a water proof tarp. I have really enjoyed it, and it gives you a better sense of what's around you in the wilderness.
In high winds however there is nothing like a good double wall tent, but just remember:
A tent may give you slightly more protection than sleeping out in the open, but not much. If a bear wants at you, the fabric of the tent is no match for his sharp claws.
Bears, both black and grizzly, have been known to cause severe damage even to buildings, high wooden fences, and even vehicles. I knew of an apple orchard that had an 8-10 ft. high wooden slat fence that a small black bear tore through to get at the fresh, ripe apples.
The point: Don't count on a tent to give you any protection. Keep your bear spray handy.
A tent can provide a psychological barrier for the bear - which won't do much to deter it if it smells something it wants inside (food), but can prevent haphazard encounters.
For example, if a bear is wandering through your camp on its way to check out your expertly hung bear hang a tent will be a visual obstacle it will naturally move around / avoid, whereas a sleeping bag out in the open is more likely to be "tripped over" and raise its curiosity.
A hammock likely will fall somewhere in between - as it is higher, and more obvious. It might provide some psychological repellent for a bear, though I would imagine less so than a tent.
And the importance of psychological protection for yourself should not be under-estimated. If you have properly secured and bear-safed your camp, then worrying isn't going to help anything. A tent provides a sense of security, and helps you get a good night's rest.
Along these lines, the "11th essential" item for me when sleeping in bear country is ear plugs.