1. ## Science Puzzles

I'll go first. Assume beakers and water volumes to be equal.

Which side will tilt down...and why?   Reply With Quote

2. Beaker with steel ball will tilt down.

Water and beakers exert equal force on the scales. If the steel ball was hanging in the air, the force on the line would be equal to that exerted by the weight of the steel ball. However, since the ball is in water, the force on the line is less in the amount equal to the gravitational force of water displaced by the steel ball. This instead is added as a force on the scale.

The ping pong ball if it was floating on the surface and not attached by a string would add its weight to the scale. Submerging it adds an upward force (making weight on scale lighter) of the ball trying to get to the surface equal to the weight of displaced water minus the weight of the ping pong ball.

At least, that's what I think will happen!  Reply With Quote

3. Ping pong ball goes up. Since the steel ball is suspended we can subtract the mass (assuming water) of the volume displaced. The resulting total mass will necessarily be less than the mass of any actual object of equal volume in the same vessel/amount of water.  Reply With Quote

4. The ping pong ball will go down, because ping pong balls have weight (added downward force) while suspended steel balls don't.

Edit: If you don't believe me, imagine setting up a second scale, putting just the water on the first scale, and just the balls on the second scale. If you believe that the total mass is equal to the sum of the parts, then this technique should show you the answer.

Puzzle (Too lazy to make a picture):

Suppose I'm in a car with a helium balloon tied to the passenger seat so that it's suspended above the seat. When I push on the gas pedal, which way do I see the balloon moving relative to the seat?  Reply With Quote

5. I'm guessing that the weight of the left side is equal to the weight of the water (which would be the same on both sides, since we can assume the levels are the same, and the two balls are exactly the same size, thus displacing exactly the same volume of water) + the weight of the ping pong ball and string, which while less dense than water, are not less dense than air, so it would be a small positive number. The force of the ball trying to rise would have no effect, as it would be like lifting yourself.

I'm guessing that the weight of the right side is equal to the weight of the water + whatever small amount of force the water has on the steel ball (the ball weighs less in water than in air, so the water does push against the steel ball in some small amount.. ie.. if the string was attached to an additional "fish scale" on the pole it's dangling from, it would weigh less while submerged in the water than not, therefore the water is taking on some small amount of the steel balls weight).

So.. in summary, if the weight of the ping pong is greater than the amount of support the water is giving to the steel ball.. the left side goes down. If the support the water is giving to the steel ball is greater than the weight of the ping pong ball.. the right side goes down (discounting the different lengths of string submerged as too small to worry with, anyway).

So.. I guess you'd need to calculate the buoyancy of steel in water vs the weight of the ping pong ball. I'll go with the water supporting far more steel ball than the ping pong ball weights.

RIGHT SIDE GOES DOWN.

Edit: Correction, since the steel ball is negatively buoyant in water, the water would push up on it with the equivalent of the steel balls volume in water. (I suspected this, so I just looked up buoyancy and confirmed). So basically, the right side weighs exactly the weight of a same size ball of water - the weight of the ping pong ball MORE than the left side.

So.. RIGHT SIDE GOES DOWN. I'm now 99.99% sure.  Reply With Quote

6. I don't think the steel weight can add any weight to the right side no matter how one describes it. So its left side down because of weight of the ping pong ball. The string may add a small buoyancy.

Correction: The string would NOT add a small buoyancy, duh  Reply With Quote

7. They're equal; the balance does not move.

The beakers of water should be viewed as enclosed systems. It doesn't matter what's inside, only how much force each beaker of water exerts on its arm of the balance. Assuming there aren't any trick variables ("the right one is oil not water hurr hurr"), those forces will be the same.

The ping pong ball does not matter (if we assume that it is massless) because the force it exerts on the cable (also assumed to be massless) is balanced by force from the water it displaces. You can also view this as a potential energy thing. The ping pong ball gains PE from its buoyancy, but the water gains the same PE from being displaced upward.

The steel ball doesn't matter either because it's not connected to the arm of the balance. So all it's doing is displacing water. Would a narrow, tall beaker that has the same volume weigh any more or less? Nope. Same idea.

If we're in the real world then the string and the ping pong ball would have mass and so the left side would go down.  Reply With Quote

8. Originally Posted by 99Problems I don't think the steel weight can add any weight to the right side no matter how one describes it. Originally Posted by rhinosaur The steel ball doesn't matter either because it's not connected to the arm of the balance. So all it's doing is displacing water. Would a narrow, tall beaker that has the same volume weigh any more or less? Nope. Same idea.
http://en.wikipedia.org/wiki/Archimedes'_principle

Just combine Archimedes principle with Newton's third law.  Reply With Quote

9.   Reply With Quote

10. @99Problems that's a valid point for the ping pong ball, but the steel ball is not connected to the truck.  Reply With Quote

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