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# buoyancy force problems

From Wikipedia

Buoyancy - Wikipedia, the free encyclopedia

In physics, buoyancy is an upward acting force exerted by a fluid, that opposes an object's weight. If the object is either less dense than the liquid or is ...

Question:Is it true about mountains that they balance the forces of gravity and buoyancy? Because they have deep crustal roots fixed in mantle. Do they balance the earth's crust in this way? I am not talking about earthquakes.

Answers:Tall mountains have deep roots. This is the Principle of Isostacy. Since mountains have thicker crust, they "float" on the mantle somewhat like an iceberg floats in the ocean. Since the mountains are not moving they are at equilibrium, which means the downward forces are equal (and opposite) to the upward forces. When crust thickens the underlying mantle is displaced. This is due to the plastic nature of the mantle, which is a solid that is able to flow in response to the placement of mountains. I could go into the mathematics of isostacy but I won't.

Question:I know that that buoyant force equals the amount of liquid displaced but if the shape of an object is changed, and it still has the same volume then will the amount of buoyant force change? I'm really confused about this. Thank-You

Answers:Where you are getting confused, I think, is in the word volume. If you take a cube of steel of, say, 1 cubic meter, in size, and reshape it into a shape of a boat, the volume of steel is still 1 cubic meter, but the volume enclosed by that 1 cubic meter can be many thousands of cubic meters. And therefore the cube will sink and the boat will not.

Question:How do I find the answer to this question? Once I find the answer, how do I find out how many pounds this is? I am confused about the formula you use to find this. Can anyone one explain it is simple terms?

Answers:Remember F=ma. Mass =560kg, acceleration is the force of gravity. 9.8m/s^2. 5488 Newtons, which is kgm/s^2.

Question:I need to design a cofferdam to stop water flow to facilitate the repair of 4m (15ft) high gate in a large water system. For starters, this cofferdam would have to be a u-shaped structure with rubber seals on the two sides and the bottom. It would hold the water and stop it going to the other side. While I am taking care of the structural design to withstand hydrostatic forces, I think it should also be designed for buoyancy forces. The channel to be closed is about 3.5 m wide and 4 m deep. The depth of the U shape is about 0.6 m. (The cofferdam cannot be flat as I need to provide some working space). Due to this depth, I calculated that it would displace approx. 8.4 tons of water and experience buoyancy force due to its sealing at the bottom. I also calculated there would be about 5 tons of frictional force at concrete wall to rubber seal (using 0.3 wet coefficient of friction) due to hydrostatic force acting on the seals. 1) Is my assumption correct in considering buoyancy effect? The estimated weight of the cofferdam (preliminary design) is about 4 tons. Should I increase the steel weight to more than buoyancy force? 2) Should I take advantage of the frictional force (between the wall and rubber seals) that existed due to hydrostatic force on the cofferdam? (This is a hydraulics/civil engineering question) 3. Any suggestions in general or further reading?