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Re: Test question



Herb has now almost defined the problem to the point it can be answered.

Here are the data:
(1) The cup will sink when the second block is added.
(2) The density of the cup material is greater than the density of
water.

Data yet required, along with my assumptions:
(3) Needed: the density of the wood blocks. Assumption: the wood blocks
are both less dense than water.
(4) Needed: the volume of the cup material. Assumption: less than the
volume of water displaced by the second floating wood block.

Answer with given assumptions:
The water level rises.

Logic:
(a) Each wood block displaces its weight's worth of water whether it is
in the cup or floating by itself. Therefore, it does not make any
difference whether the wood is in the cup or not.
(a1) Adding the second block directly to the water will make the water
level go up.
(a2) Adding the second block to the cup would make the water level go up
if the cup did not sink.
(a3) (tangential comment) Taking the first block out of the cup and
floating the block directly in the water will not change the water level
assuming the cup stays floating.

(b) The cup, being made of material more dense than water, displaces its
weight's worth of water when it floats, but displaces its volume's worth
of water when submerged. Therefore, it displaces more water when
floating than when sunk.
(b1) Sinking the cup (without adding the second block) makes the water
level go down.
(b2) Sinking the cup by adding the second block makes the water level go
up if the volume of water displaced by the second block is more than the
difference between the cup's mass and the cup's material volume.
(b3) Sinking the cup by adding the second block makes the water level go
down if the water displaced by the second block is less than the
difference between the cup's mass and the cup's material volume.
(b4) Sinking the cup by adding the second block does not change the
water level if the water displaced by the second block is the same as
the difference between the cup's mass and the cup's material volume.

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Chair of Sciences
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu

Assume that a plastic cup and very small block of wood
inside are just floating on the surface of water in a large jar.
The density of the plastic cup is greater than the density
of the water and the rim of the plastic cup is only one
"RCH" above the surface with the rest of the plastic cup
below the surface.

When a second small block of wood is added, its weight
is just large enough to sink the plastic cup.

Will the level of the water in the large jar rise, sink,
or remain the same after the cup sinks to the bottom of the jar?

Herb