1. A scientist proposes construction of a space elevator by using a steel wire to raise a mass from the Earth's surface to a satellite 1000 km above the Earth's surface.
Assume the steel wire has a diameter of 1 mm.
a) What is the mass of the wire?
b) Estimate the extension of the wire due to its weight. Assume that all parts of the
wire experience the same acceleration of gravity as at the surface of the Earth.
c) Is this realistic?
2. Greenland Icecap
a) Estimate the rise in sea level if the Greenland ice cap fully melts.
b) How much does your answer change if you also consider the melting of ice in the
waters surrounding Greenland?
3. A cube having volume 100 cm3
floats in water.
a) If 70% of the cube is submerged, what is its density?
b) The cube is next placed in an unknown liquid and 90% of it is submerged. What
is the density of the liquid?
4. A water tank has a small hole near its bottom at a depth h from the top surface. What
is the speed of the stream of water emerging from the hole?
5. Gas Pressure
a) Estimate the density of air at sea level and a temperature of 20 o
C.
b) Consider a nitrogen molecule travelling at the speed of sound that bounces
perpendicularly off the wall of a chamber. Assume its speed is not changed while
its direction is reversed. What momentum is transferred to the wall?
c) Estimating the number of collisions per m2
per second with the wall by
multiplying the half the particle density times the speed. (The factor half takes
into account that the molecules move randomly and only half have a velocity
component toward the wall.)
d) Estimate the gas pressure.