Buoyancy Question

[v4runc00l]

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I had a quick question on the Physical Science section question number 26 on AAMC Practice Test #8. For that question, I set the Boyant Force = m(lead)*g. From there, I set m(lead)=rho(lead)*V(lead). When plugging it in and solving for Buoyant Force I got answer choice C which is wrong. Why can I not equate the force of gravity and buoyant force in this case? Would I only be able to equate it if the object was fully submerged in water and not moving? Thanks a lot!

 

[phltz]

The mass of lead times g will give you the force of gravity pulling down on the lead, not the buoyant force up on it.

Buoyancy is the weight of the water displaced. By "water displaced", we basically mean that if we could teleport the lead mass out of the water, there'd be a hole in the water shaped just like the mass for a split second, before the hole collapsed. That hole can be thought of as space where there should be water, but isn't. It's water that's been displaced. And it has the same volume as the volume of the lead mass.

So what you need is to find the weight of the water displaced. Which would be rho*V*g. Just like you calculated. Only use the rho of water instead of lead.

 

[v4runc00l]

I know but in a force diagram isn't the force of buoyancy equal to the force of gravity.. therefore, shouldn't we be able to set them equal to each other and solve that way?

 

[loveoforganic]

buoyant force and force due to gravity are only equal if an object is floating