Buoyant force calculation - please help :)?

Question

You're told the volume of a lead weight that is sitting at the bottom of a tank floor; the tank is filled with water. You're given the density of the water and of the lead. What is the buoyant force that the water exerts on the lead weight? I thought it would be equal to the weight of the lead (mg), but it is equal to (row)(g)(vol). I understand why it is equal to (row)(g)(vol), but why is the buoyant force not also equal to mg? And what effect does sitting on the bottom of the tank rather than floating have?

Thanks!

Answer 1

The buoyant force is not equal to m*g of the object...buoyant force is equal to the weight of the fluid (in this case = water) displaced (which could be thought of as m*g of the water displaced).

Rho * volume gives you a mass, and g is the acceleration due to earth's gravity, so it is the same as m*g of the water displaced.

If the buoyant force is greater than the weight of the object, then it will float.  If Fb is equal to the weight of the object, then it may be suspended somewhere in the water column.

If the buoyant force is less than the weight of the object, then the object sinks.

If an object is floating at the surface (partially submerged), then it isn't really displacing an amount of water equal to its total volume...rather, it is displacing an amount of water equal to the volume of the object below the surface (think iceberg).

I hope this helps!

Answer 2

mg is the weight of the lead.



A body sitting at at the bottom of the tank displaces only a volume of water equal to its volume. The weight of displaced water, which is the buoyancy, is equal to the density of the water times the volume displaced, hence it is not equal to the weight of the lead.

The lead can not float simply because it can not displace a volume of water whose weight is equal to its (the lead) weight.

A floating body displaces a volume of water that weighs the same as the weight of the body.

Answer 3

Archimedes'principle says that the buoyant force is equal to the weight of the water displaced; in other words, the volume of the weight times g times the density of water.  It doesn't depend on the weight of the lead.  Of course, lead being heavy, it won't float.  It will just be a bit lighter than it would be in air.  In the case of a floating object like a boat the buoyant force will be equal to the weight of the water displaced, that is, the density of water times g times the volume of the part of the boat below the waterline.

Answer 4

boyont force of displaced water would be equal to the force of the displaced water.  It would be the same unless it is floating in which case it is displacing less water.

A 1 cubic foot ballon and a 1 cubic foot cannon ball have the same boyont force in the water, the balloon will rise since the force overcomes the force of gravity, while the cannon ball will still sink like a rock.

Answer 5

Any object either floating on the surface or completely submerged in a fluid will experience a buoyant force. The reason any object floats is due to the buoyant force. So let's use water as the fluid responsible for the buoyant force since that is what your example uses.  The magnitude of the buoyant force caused by water will always be equal to the mass of water displaced multiplied by the gravitational constant g. That is:

Fb = m(water displaced)*g

The formula (rho)(g)(V) is actually the exact same formula as what is written directly above.

m(water displaced)*g *V / V  

(rho)(g)(V)

I just multiplied the top and bottom by V. V just represents the volume of water the object in your water is displacing and rho is the density of water.

So I think where your confusion might be is that multiplying the mass of the lead by the gravitational constant (mass of lead * g)  gives you the force on the lead due to gravity, NOT due to the buoyant force. While the lead is in water it still experiences gravitational force (that causes it to sink). The reason the lead sinks is because its gravitational force is greater then the bouyant force. Additionally, it goes slower in water then in air because  the buoyant force is pushing up on it.  

As for the second part of your questions. There is actually no difference at all if your lead object is sitting at the bottom of a tank or if it is in the process of sinking in middle of the water. The mass of the water it displaces is exactly the same no matter where it is (unless you go into extreme deep water where in fact the density of water increases because of lower temperatures). Where you run into complications is when an object is floating. It should be obvious that when an object floats, it displaces less water then if it were completely submerged. The only way an object can float is if the bouyant force is equal to the mass of the object times g. In other words is must displace a  mass of water equal to it's own mass. That is exactly how something as large as a cruiseship floats. The ship simply displaces a mass of water equal to it's entire mass.

Answer 6

Keep in mind that when the lead weight is submerged the buoyant force is acting on the entire lead weight..However when it is only partially submerged, it is only acting on the portion that is underwater.