Weighing Floating Cork: Does Upthrust Affect Weight?

[rishch]

Suppose you have a beaker containing some water and you weigh it using a weighing scale (the ones you use to measure your own weight ) and its weight is x.You also have a cork which has a weight y.Suppose you put the cork in water and it floats and you then place the beaker with the cork floating in it on the weighing scale.Would its weight be x+y or would the upthrust on the cork affect the weight of the entire system?

 

[Doc Al]

Would its weight be x+y or would the upthrust on the cork affect the weight of the entire system?

What do you think?

 

[rishch]

I think that the weight wouldn't be affected.

 

[Doc Al]

I think that the weight wouldn't be affected.

So you think you can support beaker + water + cork with the same force as you do just beaker + water?

Since the system of beaker + water + cork is in equilibrium, the net force on it must be zero. Gravity pulls down with the full weight of all the mass; so the scale must push up with an equal force.

 

[rishch]

Thanks !

 

[Doc Al]

Another way to think of it:

Since the cork is floating, there must be an upward buoyant from the water acting on the cork that is exactly equal to the cork's weight. But by Newton's 3rd law, if the water pushes the cork up, the cork must push the water down with an equal and opposite force. That downward force on the water adds to the upward force that the scale must exert to support the water.

 

[rishch]

Since the cork isn't actually in contact with the weighing scale then how does the force of gravity acting on the cork get transferred to the scale?

 

[Doc Al]

Since the cork isn't actually in contact with the weighing scale then how does the force of gravity acting on the cork get transferred to the scale?

In the same manner as this: Imagine you were standing on a scale. It reads your normal weight. Now someone balances a book on your head. Now the scale reads your weight plus the weight of the book. The book is not in direct contact with the scale, so how does the scale 'know about' the book on your head?

The book pushes down on your head with a force equal to its weight. Thus, to support you the scale now has to exert a greater force than just your weight, since it must counter balance the added force from the book on you as well as your weight.

With the cork and water it's the same idea. The cork pushes down on the water just like the book pushes down on your head.

Make sense?

 

[rishch]

So the weight of the book gets transferred to the scale through you?

 

[Doc Al]

So the weight of the book gets transferred to the scale through you?

Sure. No magic here!