Calculating Buoyant Force Using Archimedes' Principle

[blacklily28]

Homework Statement

An object weighing 5.0 Newtons displaces a certain volume of water when dropped into a large beaker of water. The weight of the displaced water is 3.5 Newtons. The object is free to sink or float. What would be the value of the buoyant force is another object twice the volume, but having the same weight, was droppen into the large beaker of water? The object is free to sink or float

I believe the buoyant force is 3.5 Newtons, judging from Archimedes' Principle which states that "an object immersed in a fluid experiences a buoyant force equal to the weight of the water displaced." I'm not sure if this is correct, going by volume and not weight.

 

[Doc Al]

An object weighing 5.0 Newtons displaces a certain volume of water when dropped into a large beaker of water. The weight of the displaced water is 3.5 Newtons. The object is free to sink or float.

The first thing to decide is whether it sinks or floats. Well?

What would be the value of the buoyant force is another object twice the volume, but having the same weight, was droppen into the large beaker of water? The object is free to sink or float

Does that one sink or float?

 

[blacklily28]

They both sink.

 

[Doc Al]

They both sink.

Explain your reasoning.

 

[blacklily28]

Because an object will float if the buoyant force (3.5 N) is greater than the weight of the submerged object (5 N) - so in this case the object would sink.

But does the buoyant force change if the volume is doubled?

 

[Doc Al]

Because an object will float if the buoyant force (3.5 N) is greater than the weight of the submerged object (5 N) - so in this case the object would sink.

Good. This means that the entire volume is underwater.

But does the buoyant force change if the volume is doubled?

What matters is the volume of the object that is under water.

Hint: If this second object were totally submerged, what would be the buoyant force on it?

 

[blacklily28]

3.5 N?

 

[Doc Al]

3.5 N?

No. Recall that, per Archimedes' principle, the buoyant force equals the weight of the displaced fluid. The first object was totally submerged, thus it displaced an amount of water equal to 3.5 N. But the second object has twice the volume. So if that second object were totally submerged, it would displace twice the water. How much buoyant force would that equal?

Does the second object float or sink?

 

[blacklily28]

It would float- so 5 N?

 

[Doc Al]

It would float- so 5 N?

Right. If the 2nd object were totally submerged it would displace twice the water and thus have twice the buoyant force: 7 N. That's more than enough to support its weight, so it will float only partly submerged. Since you know it floats, its buoyant force must equal its weight = 5 N.

 

[blacklily28]

Thanks!