# Document 11657139

```Physics 53
Summer 2010
Quiz 7
Solutions
1.
A cylindrical block of wood floats as shown in a container of
water. The block has uniform density 60% that of water. Which of
these is wrong?
The block floats with 60% of its volume under water.
If it is pushed down and released, it will execute
simple harmonic motion vertically.
√
If the system is in an elevator accelerating upward the
block will sink lower in the water. [No change.]
The buoyant force on the block is equal to its weight.
Check T or F depending on whether the statement is true or false.
2.
The pressure in a stream emerging from a nozzle is greater than that emerging
from the hose without the nozzle.
T
√
F
[Both are air pressure.]
1
Physics 53
3.
Summer 2010
A block of mass m is attached to a spring of stiffness k
as shown. It slides on a frictionless table. It is pushed
to the left, compressing the spring through distance
A0 and released from rest. The next time it is at that
location, momentarily at rest, an identical block is
gently placed at rest on top of it. There is static friction
between the blocks, with coefficient &micro;s .
a.
Which of these quantities is changed by the addition of the new block
(assuming &micro;s is large enough to keep the blocks together)? Amplitude,
angular frequency, total energy.
b.
Give the old and new values of the one(s) that changed.
c.
How large must &micro;s be for the blocks to stay together?
a.
Angular frequency (only).
b.
ω 0 = k /m , ω = k / 2m .
c.
The maximum acceleration of the spring system is ω 2 A0 . The maximum that
friction can provide the upper block is &micro;s g , so we must have &micro;s ≥ ω 2 A0 / g .
2
```