Battleship Floating in a Bathtub?

Question

I love physics puzzles. Einstein called this type of physics gedanken physics because it required a person to use his or her mind to work through the problem. What follows is one of my all-time favorites.

Can a battleship float in a bathtub? Of course, you have to imagine a very big bathtub or a very small battleship. In either case, there is just a bit of water all around and under the ship. Specifically, suppose the ship weighs 100 tons (a very small ship) and the water in the tub weighs 100 pounds. Will it float or touch bottom?

a) It will float if there is enough water to go all around it.

b) It will touch bottom because the ship's weight exceeds the water's weight.

What do you think?

Answer 1

It will touch bottom and then some. A 100 ton ship will only float if the force exerting on the hull is the same as the weight of the ship. The force can be measured as the weight of the water displaced by the hull. In this case, the hull will need to displace 100 tons of water. This is impossible if the weight of all the water in the tub is only 100pounds.

Answer 2

A body of weight W will float if and only if the weight B of the water it displaces is equal to W. That is, your 100 ton BB will float only if it displaces 100 tons of water. [BB is the US Navy's designator for battleship...as in BB-60 for the USS Iowa.] a) Yes if you have at least 100 tons of water to displace. b) No if you have more than 100 tons of water available to displace. [Actually, I would guess the keel might barely touch the tub if there was just barely 100 tons to displace in the tub.] Here's the physics in a nutshell...f = ma = W - B; where f is the net force acting on your BB of mass m, W is its weight W = mg and B is the opposing force called buoyancy. B = rho g V; where rho is water density, g is acceleration due to gravity and V is the volume of water displaced by the BB Thus, to float, we need f = ma = W - B = 0; so that W = mg = rho g V = B. f, the net force, has to be zero because, otherwise, the battleship would be accelerating (a <> 0)...either sinking further or bobbing up. Either way it would not be just floating which means its vertical velocity is zero.

Answer 3

a) If the tub is adequately designed, the water will rise about the sides of the ship until the pressure on the bottom of the ship is sufficient to bear it up. At this level, the "hole" in the water will weigh as much as the battleship with a "surplus" of 100 lb.

Answer 4

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Answer 5

a

the design of these ships is such as to get maximum up thrust in AIR....in water it sud be unimaginably high coz its density is more

so this ship disperses its weight around