What will be the weighing machine's reading?

[Ravi Singh choudhary]

Suppose a container is full of water is placed over a weighing machine. Now a ball is hanged with massless string but dipped inside the tank and ball is not touching the bottom. What will be the new reading on the weighing machine?

 

[Doc Al]

What do you think?

 

[Ravi Singh choudhary]

Weighing machine measures the normal contact force between container and the machine. Now when ball is dipped with string. I got lost in free body diagram.

 

[Doc Al]

Weighing machine measures the normal contact force between container and the machine.

Good.

Now when ball is dipped with string. I got lost in free body diagram.

What if there were no string. You just dropped the ball into the container. What would the scale read then?

Now suspend the ball by the string. How would that change your free body diagram? What forces act on the ball?

 

[Baluncore]

If the ball density is less than water, the ball will float. In that case the string will carry no weight and the scale reading will rise as it includes the whole weight of the floating ball.

But if the ball density is higher than water, it will sink below the surface. The pressure of water on the ball will then be more on the bottom of the ball pushing up, than on top of the ball pushing down. That is because hydrostatic pressure increases with depth. Will the string then carry less weight and the scales carry more?

 

[A.T.]

Weighing machine measures the normal contact force between container and the machine. Now when ball is dipped with string. I got lost in free body diagram.

What happens to the water level with the ball submerged? How are water depth and hydro-static pressure onto the bottom related?

 

[Ravi Singh choudhary]

If the ball density is less than water, the ball will float. In that case the string will carry no weight and the scale reading will rise as it includes the whole weight of the floating ball.

But if the ball density is higher than water, it will sink below the surface. The pressure of water on the ball will then be more on the bottom of the ball pushing up, than on top of the ball pushing down. That is because hydrostatic pressure increases with depth. Will the string then carry less weight and the scales carry more?

I got the logic of no string. The ball sink or float; in both cases weighing machine will read higher weight. With string but ball has lower density then again weighing machine will read more. Finally in the case of ball of higher density with water but with string; string will have some tension force upward plus buoyant force too that will balance the weight of the ball. But again got lost in weighing machine reading in last case.

 

[Ravi Singh choudhary]

What happens to the water level with the ball submerged? How are water depth and hydro-static pressure onto the bottom related?

Water level will increase. There is a linear relationship between pressure and depth. Depth multiplied by specific weight is hydrostatic pressure, so pressure will increase.

 

[ZapperZ]

You are losing focus here.

Go back to the free-body diagram. Knowing what you know now, can you show a drawing of the free-body diagram with all the relevant forces involved to be able to figure out the weight being read by the weighing machine?

Zz.

 

[Doc Al]

To add some additional focus, choose the 'container + contents' as your system. Compare three cases:

1) Container + water (no ball)
2) Container + water + ball (just toss the ball in, no string)
3) Container + water + ball suspended (there's a string)

Compare the forces acting on your "system" in each case.