Originally posted by talzamirI'm going to go with "nothing" (neglecting dynamic effects).
There are several stainless steel ball bearings on a piece of wood. The piece of wood is floating in a kettle filled with water all the way to the rim. One by one the ball bearings are pushed off the edge of the piece of wood so they fall into the water. What happens to the water level in the kettle?
Originally posted by joe shmoMy latest
I'm going to go with "nothing" (neglecting dynamic effects).
edit: well...maybe not
Originally posted by joe shmoThat result does not seem right to me.
the change in height will be a function of the relative densities of the bearing and liquid
delta_h = V_b/A*((rho_b - rho_liq)/rho_liq)
A = cross sectional area of tank
V_b = volume of bearings
rho_liq = density of liquid
rho_b = density of bearing
delta_h = change in height
which says as long as the density of the bearing is greater than that of the liqiud delta_h will be positive.
Originally posted by LemonJelloYeah, I agree...something is wrong with my analysis. Incedentally, thats a nice tidy way to think about it...and it gives the result. Guess we will wait and see if the OP closes the case?
That result does not seem right to me.
If on the wood, a bearing should displace an amount of water that has mass equal to the bearing's mass; on the other hand if sunken in the kettle, a bearing should displace an amount of water that has volume equal to the bearing's volume. So when rho_b > rho_liq this latter amount is smaller and delta_h should thus be negative, no?
Originally posted by talzamircauses the water level to again drop.
The truth of the matter has been found in the above discussion, as has the reason for it. While the ball bearings are on the piece of wood, they displace enough water to equal their own mass; while underwater, enough water to equal their volume.
Let V_ballbearing be the volume of a ball bearing and rho_steel its density. Their mass is therefo ...[text shortened]... salt into the water do to the water level when the piece of wood is still floating in the water?