# Question on upthrust

1. Jul 27, 2009

### leena19

1. The problem statement, all variables and given/known data

2 small metal spheres of the same size but made of aluminium and brass are released simultaneously from rest inside a tall vessel filled with a viscous liquid.Consider the following statements
A) Upthrusts on both spheres are the same
B)The initial accelerations of both spheres are the same
C)Both spheres will attain the terminal velocity at the same depth.
Of the above statements
(1)only A is true (2) only B is true (3)only C is true (4)only A and B are true (5) all A,B and C are true
2. Relevant equations
Upthrust = mg = V*rho*g ?

3. The attempt at a solution

I first thought only B was true.that the initial accelerations would be the same,but I guess the initial accelerations would depend on their weights which are not equal so the initial accelerations cannot be the same?

But I don't get why A is true.Doesn't upthrust depend on the weight of the spheres which are different in this case,but if we consider=V*rho*g ,the upthrusts would be the same since the volumes and the density of the liquid are the same ?Why the difference?

And just to verify, C ) is wrong cause the initial accelerations are different ,therefore the initial velocities of the spheres are different,so they would attain terminal velocity at different depths?

2. Jul 27, 2009

### minger

No, the drag force, or upthrust as you're referring is merely a function of an objects shape, and the fluid through which it passes. As both balls are the same size and shape, and both falling through the same liquid, their drag forces will be equal as well.

c) is not correct because the forces don't balance at the same condition. Terminal velocity is the point which an object no longer accelerates due to gravity. Since it's no longer accelerating, all forces on it are equal. Since we just seen that the weight forces are not equal while the drag forces are, they will reach equilibrium at different points.

3. Jul 27, 2009

### leena19

Thanx minger!
I understand now.

4. Jul 27, 2009

### turin

Hmm... I basically agree with minger, except it seems that bouyancy is neglected. Bouyancy is not a drag force. In other words, the upthrust could be due to a combination of drag and bouyancy. Both of these effects are relatated to the size and shape of the object, so anyway the ultimate conclusion is the same.

5. Jul 28, 2009

Agreed.