Physical Sciences 2 Section Problems #7 1. A copper wire d = 1 mm in diameter is
attached to a wall at one end and stretched
over a pulley, as shown. The length of the
horizontal portion of the wire is L = 2 m.
(You may neglect the vertical portion.)
Hanging from the other end of the wire is a
mass m = 5 kg. Copper has a Young’s
modulus of Ecopper = 110 GPa.
a) The tensile strength of copper is 220 MPa. Will the wire break?
b) By how much is the wire stretched from its relaxed length?
c) If the mass were displaced vertically from equilibrium by a (very) small amount, it
would begin to oscillate up and down, because the wire would act like a spring. What
would be the period of the oscillation?
1 Physical Sciences 2 Section Problems #7 2. Pressure puzzlers:
a) Is the pressure at point A higher, lower, or the same as the pressure at point B?
b) Hoover Dam holds back Lake Mead, which is about 600 feet deep and 115 miles long.
Consider the horizontal force that the water exerts on the dam. How much smaller would
this force be if Lake Mead were replaced with “Lake Mudd,” which is 600 feet deep but
only 115 inches long?
3. If your eardrum will rupture when the pressure difference between inside and outside
reaches 35 kPa, how deep can you dive in water without worrying about ruptured
eardrums? (Assume that the air inside the ear remains at atmospheric pressure).
2 Physical Sciences 2 Section Problems #7 4. In lecture we used Archimedes’ principle to look at completely
submerged objects. Let’s consider the case of a partially submerged
object. You can neglect surface tension throughout this problem.
a) Show that the mass of the fluid displaced is equal to the mass of the
object for any partially submerged object at static equilibrium.
b) The idiom “tip of the iceberg” refers to the fact that, at static equilibrium, only a little
bit of an iceberg sticks above the water level. What fraction of an iceberg lies below the
surface? (You may need to know some densities: ρice = 920 kg/m3 and ρseawater = 1030
kg/m3.)
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