27 ways to use a barometer to find the height of a building
by Douglas Grimm
Tie a long piece of string to the barometer. Hold one end of the
string from the top of the building, so that the end of the barometer
barely clears the ground. Give the barometer a small displacement and
time its period as a compound pendulum.
Smash the barometer on the roof of the building and time how long
it takes for the mercury to drip down the wall of the building to the
ground. Use the known viscosity of mercury to find the velocity.
Throw the barometer horizontally off the building with a known
velocity (calibrate your throwing ability by timing and measuring
barometer throws on the ground). Use projectile motion to find the
height of the building once the distance the barometer lands from the
building is found.
Find a small, very efficient, very light electric motor. Weigh the
barometer. Use the motor to carry the barometer up the building. Using
a voltmeter and ammeter, calculate the work done by the motor, and
thus the gravitational potential difference between the top and bottom
of the building. Knowing g, find the height.
Go to the basement. Find a part of the basement such that directly
above you is solid brick until you reach the roof. Throw the barometer
at the ceiling of the basement, which is the floor of the building.
The barometer will most likely bounce off the floor. Repeat n times,
where n is a very large number. In a few trials, the barometer will
tunnel through the potential field of the bricks, and appear on the
top of the building. Calculate the percentage of trials for which the
barometer tunnels. Use the quantum tunneling equation to calculate the
length of the barrier, and thus the height of the building. Note: this
effect can be calibrated properly by finding the likelyhood of the
barometer tunneling through one brick.
Attach a copper wire to the top of the building, and attach the
other end to the ground. Smash the barometer and use one of the shards
of glass to cut the wire halfway up the building and place an ammeter
in series with the wire. Knowing the current through the wire and the
resistivity of copper, the potential difference between the top of the
building and the bottom of the building can be found. This will be a
gravitational potential difference, not an electrical one, but the
electrons don't know that. Thus, since g is known, the height of the
building can be found.
Find a large wooden rod a bit longer than the building is high.
Wrap an insulated copper wire around this rod at a uniform turn
density. Make the coil stop at the top and bottom of the building. Run
alternating current through the coil, measure current and voltage, and
determine the inductance of the coil. Place the barometer in series
with the coil so the resistance of the circuit is enough to stop the
wires from melting. With the inductance of the coil and its turns per
unit length and radius, the length of the coil, and thus the height of
the building, can be found.
Drop the barometer off the top of the building and measure the
radius of the resulting puddle of mercury.
Using a device that can propel an object at a known velocity (such
as a baseball pitching machine or a rail gun), find the escape
velocity of the barometer from the ground, after first having tied a
string to the barometer so it can be retrieved from deep space. Repeat
on the top of the building. The difference in escape velocity energies
gives the gravitational potential difference between the ground and
the roof, thus yielding the height.
Using the aforementioned pitching machine or rail gun, find the
velocity at which the barometer needs to be projected to reach the
roof from the ground.
Make a small hole in the barometer through which mercury drips at
a constant rate. Time this rate at the ground. Place the barometer on
the roof and observe the drip rate from the ground with binoculars.
The drip rate will be dilated, by general relativity, by a factor
which will give the difference in the curvature of space at the bottom
and top of the building. Knowing the mass and radius of the earth and
so on, the height of the building can be found.
THIS METHOD USES MORE THAN ONE BAROMETER: Pack as many barometers
as possible into the building until it undergoes gravitational
collapse and becomes a black hole. Knowing the number of barometers
used, the mass of this hole can be calculated, and the Schwarzchild
radius of the hole is thus half the height of the building.
Find a barometer that uses a liquid with no surface tension
whatsoever (superfluid helium?). Break the barometer and spread the
liquid evenly over the surface of the building. Measure the depth of
the resulting liquid film. Knowing the volume of the barometer, this
gives the surface area of the building, which will give its height, if
its width and depth are known.
Stand on the roof of the building. Throw the barometer to a point
exactly on the horizon. Measure the distance from the bottom of the
building to the barometer. This gives the horizon distance at the top
of the building, thus giving its height above the ground.
Make a small hole in the barometer so mercury drips out at a
constant rate. Place the barometer so that it is dripping off the roof
onto the ground. Measure the time between a drop being released from
the barometer and the drop hitting the ground. Repeat the measurement
when moving towards the ground at a known velocity. The time between a
drop being released and a drop hitting the ground will change. Using
the Lorentz transformation equations and taking the top of the tower
as x = 0, the position of the ground can be found. This will yield the
height of the tower.
Find a steel cable. Attach it to the barometer and use the
barometer as a physical pendulum to measure g. Then attach the
building to the cable (after having remove it from its foundations and
attaching the cable to a crane of some sort), and using the building
as a physical pendulum, and knowing g, measure its moment of inertia.
This will give the dimensions of the building and so on.
Use a barometer containing sulfuric acid. Break the barometer on
the roof of the building and time how long it takes the acid to eat
its way down to the ground.
Measure the volume of the barometer at the bottom and top of the
building. By knowing the coefficient of thermal expansion of glass,
the temperature difference between the top and bottom can be
calculated. Refer this to known data of atmospheric temperature as a
function of height.
Every time somebody walks into or out of the building, stab them
with the sharpened end of the barometer (after having sharpened it, of
course). Word of the 'Barometer Murderer' will eventually reach the
building's owner, who will of course be forced to sell the building.
The real estate advertisement should give the height of the building.
Knowing the density, width and length of the building, rip the
building from its foundations and place it on top of the barometer,
giving it a pressure equal to the building's weight divided by the
measurement area of the barometer. Thus the weight, and so the height,
of the building can be found.
Find the architect who designed the building, crack the (mercury)
barometer over his coffee, watch him die when he drinks it, then steal
the building's specifications, including height.
THIS ALSO REQUIRES MORE THAN ONE BAROMETER:
knowing Young's Modulus for brick, place barometers on the roof until
the roof is lowered by one barometer length. This change in the height
of the building under a known stress and Young's Modulus will give the
height of the building.
Place a cat on top of the building. Prod it with the barometer so
that it falls off the roof. See whether the cat dies when it hits the
ground. Repeat n times, where n>>{a large number}. Refer to Dr Karl
Kruszelnicki's paper on the probability of a cat dying when falling
from a certain height.
AGAIN, MORE THAN ONE BAROMETER: place as many barometers in the
building as will fit. This gives the volume, thus the height, if other
dimensions are known.
Use a machine (such as the aforementioned baseball pitching
machine or rail gun) that can hurl the barometer down from the ground
into a hole in the ground at a velocity that is only known to within a
certain tolerance. Find the smallest uncertainty in velocity, and thus
momentum, such that the barometer appears on top of the building. Use
Heisenburg's position-momentum uncertainty relationship to find the
height of the building.
Tie a string to the barometer and hang it as a plumb bob. The
string will be slightly deflected from the vertical by the
gravitational effect of the building. This gives the mass of the
building, etc.
Find at what velocity you must move upwards or downwards past the
building such that the building is contracted to the same length as
the barometer. Find gamma for this velocity, multiply by the length of
the barometer.
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