Kaplan Buoyancy Error?

[blackmarble]

Kaplan states in their chapter on fluids (Chapter 5) something which doesn't seem right to me:

"When an object is placed in a fluid, it will sink into the fluid only to the point at which the volume of displaced fluid exerts a force that is equal to the weight of the object"

Shouldn't it sink into the fluid to the point at which the buoyant force is equal to the weight of the displaced fluid, since Fbuoy = V (fluid displaced) x Density (fluid) x gravity?

---

Members don't see this ad.

 

[Chrisz]

Bro, this is not a mistake. You simply misunderstood the two forces. Buoyancy force is provided by the water surrounding the object, and it is an upward force, whilethe weight of the object is provided by gravity and downward. If these two forces have equal magnitudes, the net force will be simply zero. In this case, Fb=Fg.
Fb=Vf*Df*g=mg
Vf*Df*g=Vo*Do*g
Vf*Df=Vo*Do

 

[blackmarble]

Oh I see, thanks. So tell me if this is right, the displaced fluid will exert a buoyant force equal to the weight of the displaced fluid, and if this force is equal/greater than the weight of the displaced object, it will float (how much volume floats above the fluid is governed by the buoyant force), but if the buoyant force isn't able to match the weight of the object, it will sink.

 

[Chrisz]

You are basically correct about the buoyancy force. An object will float when the buoyoncy force is greater or equal to the weight of an object. For example, you start an object at a point where the buoyancy force is greater than the weight, the object will start to ascend, it ascends to the point where the buoyancy force balances out the weight, and it will not ascend; this is the point where the object will have some part of itself above the surface of the water. In this case, Fb=mg. If you start an object that is heavy, and the object's weight is greater than the buoyancy force, it will sink to the bottom, where the weight is balanced out by both buoyancy force and a normal force that is provided by the bottom of container. In this case, Fb+Fn=mg.