# How much does the ball weight in water

1. May 5, 2009

1. The problem statement, all variables and given/known data
An iron ball is suspended in the air by a string attached to the ceiling. This iron ball is then submerged into the a beaker of water on top of a measuring balance, such that the ball is not in contact with the base of the beaker. When the beaker of water(without anything in it) is measured with the balance, the reading on the balance is W. What is the reading on the balance with the suspended ball in it?

2. Relevant equations
Nil

3. The attempt at a solution
T=mg-u ,
T= tension of the string
mg=weight of ball
u=upthrust due to the weight of ball displaced by the water
Since this system is in equilibruim, it can be taken that nothing has been added into the beaker of water. So, the reading on the balance with the suspended ball in it should be W.
But the answer given is W+U. Can anyone tell me what i have done wrong? Is there anything wrong with my assumption? Or is the answer really wrong? Help~~~~~

Last edited: May 5, 2009
2. May 5, 2009

### skand

write the eqn for beaker and ball as a system and note that the only force acting on them is the force of tension in string(connected to ball)and Normal(the weight measured)

Find tension using eqm of ball

3. May 5, 2009

### fatra2

Hi there,

You should forget about the gravity, otherwise you would have an unbalanced equation.

Cheers

4. May 5, 2009

### davieddy

What force does the water exert on the ball?
Now apply Newton's Third Law.

5. May 5, 2009

oh man i still dont understand........

6. May 5, 2009

there is upthrust. So do u mean the there is a equal but opposite force which is equal to the magnitude of upthrust acting on the ball? if it is so wouldnt the tension equals to the weight of the ball ie. T=mg?

Last edited: May 5, 2009
7. May 5, 2009

### fatra2

Hi there,

No that's no correct. But since the ball suspended is montionless (I suppose), then the force have come to an equilibrium. $$\sum \vec{F} = 0$$

Then, you need to see what are the forces acting on this system.

8. May 5, 2009

I can only think of the weight of the beaker of water...
so do u mean that the balance's reading is the same irregardless of whether the suspended ball is present, since the force have come to equilibrium?

9. May 5, 2009

### davieddy

The water exerts an upthrust on the ball.
Newton's Third Law tells us that the ball exerts a downthrust on the
water equal in magnitude.

10. May 5, 2009