HW#12a
Note: numbers used in solution steps are different from your WebAssign values.
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Problem 1,
Inside the boat with the person are several blocks of wood. Suppose the person now throws the
blocks of wood into the pool.
(a) Does the boat float higher, lower, or at the same level relative to the water?
higher
Key:
The boat is now carrying a reduced weight. It needs less buoyant force, hence it displace less water.
Therefore, it floats higher relative to the water.
(b) Does the water level in the pool increase, decrease, or stay the same?
stay the same
Key:
Because wood floats, before and after throwing the wood out, the weight of the total displaced water (=the
buoyant force) is always equal to the total weight of the boat, person and wood. Hence the total displaced
(occupied) water volume do not change.
Or, you can say that he water level in the pool remains the same because the blocks of wood displace the same
amount of water whether they are in the boat or in the water. In either case, they are floating, so that they
displace a volume of water with a weight equal to their weight.
If a piece of stone was thrown out, it is different.
In part a, the boat will raise a lot and displace much less
water. For part b, however, the stone will sink and not displace as much water. When it is inside the boat, the
water volume displaced due to the stone was much larger than the stone’s volume. When it is outside the boat,
the water volume it displaces is only equal to the stone’s volume.
When the stone is out of the boat, the weight
of the total displaced water (= the total buoyant force on boat and stone) is less than the total weight of the boat,
and stone. The total displaced (occupied) water volume decreased and water level will drop.
Problem 2.
An airtight box has a removable (massless) lid of area
2
·10
-2
m
2
. A
lid is placed on it while it is on top of a mountain (where P
atm
=
0.87
·10
5
Pa). It is
then taken to sea level, where P
atm
= 1.013·10
5
Pa. How much force will be
required to remove the lid?
N
(How would you do this if the lid had mass, and this value was given?)
Solution.