The Prime Directive

Kirk had beamed to the surface of a planet resembling Sun Valley, Idaho in order to accomplish the Prime Directive and check out the local babes. As they strolled past a sheer rock wall, he and Spock noticed a Klingon engaged in bungee-jumping. Spock noticed that simply by hanging at rest in his harness the Klingon had caused the cord to stretch by 7 paces. "Fascinating, Captain," declared the Vulcan half-breed, "We can predict his oscillation period at jump-time."

Ans: The Klingon dangles 7 paces, 0.007 mile. To find his mass over the spring constant, one divides by g = 17.6 mile/sq.minute. This gives m/k = 4E-4 sq.minute, of which the sqrt is 2E-2 or 0.02 minute. One full bounce takes 2pi times that.



Singapore red light district

Kirk has beamed down to Singapore because one of the houses there is famous all over the universe. While visiting the house on previous occasions, Mozart's librettist Lorenzo Da Ponte invented an anti-gravity machine and installed it in one of the rooms, where the machine eliminates the effect of the earth's gravity.

On entering this room, Kirk and Spock discover everyone floating upwards or bounding slowly off the ceiling as if in a gentle upwards gravity. They are expiencing the centrifugal effect of the earth's rotation. What is the acceleration due to this false gravity?

Ans: In TM we work in miles and minutes. The Earth's 3940 mile radius and 1600 minute day---254 minutes to turn a radian.
So the centrifugal effect is 3940/254^2 = 0.06 mile per sq.minute.

Note: Since felt gravity is 17.6, that which would be experienced without the effect of rotation is 17.66 mile/sq.minute---just adding on the 0.06.


Spock computes the mass of the earth.

Kirk is visiting a famous house of entertainment in Singapore. Spock is waiting for him in a charmingly decorated parlor and, to pass the time, decides to calculate the mass of the Earth.

Ans: Spock knows that equatorial radius is 3940 miles and equatorial gravity without the centrifugal effect is 17.66 miles per sq.minute. The universal gravitational constant G has the value E-15 in TM units.

Spock squares the radius, multiplies by 17.66, and divides by G to get the mass of the earth in talents.

3940^2 x 17.66 x E15 = 2.74E23 talents.

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The wheel rising into the air

Lawrence of Arabia is riding his camel rapidily across the desert. At the moment he is being pursued by Turks who are angry that Lawrence has placed a charge of dynamite in a culvert beneath the tracks and damaged their locomotive.

With nothing to do except evade the Turks, Lawrence recalls the beautiful sight of a wheel from the locomotive sailing 10 paces up into the blue desert sky and idly wonders the speed with which it emerged from the explosion.

Ans: Twice the height is 0.02 mile. The speed is the sqrt of what is obtained by multiplying this by the local acceleration of gravity. Sqrt of 17.6 x 0.02 is 0.6 miles a minute.

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A farm in Africa 1910

The Baroness Blixen (who wrote under the name Isak Dinesen) had a farm at the foot of the Ngong Hills, a hundred miles south of the Equator in Kenya.

In September at the time of the coffee harvest, the Baroness and her friend Denys Finch-Hatton used to watch the sun set.

Finch-Hatton had a suede antelope-skin vest with a watch pocket in which reposed a brass pocketwatch telling time in Talent-Mile minutes. On that occasion he observed that the sun took 2.37 minutes to set from the first moment it touched the horizon till the last sliver of orange disk disappeared.

How far are we from the sun, measured in solar radii?

Ans: Finch-Hatton happened to know that the earth takes 255 minutes to turn a radian relative to the sun. So he reasoned that our distance from the sun is 255/2.37 solar diameters, or 215 times the sun's radius.

That night the Baroness dreamed that she stood on a surface shining 215^2 brighter than the ground ever gets in Kenya, even with the sun directly over head. In her dream she knew that she was standing on the sun.

I am consolidating these threads of T-M physics problems. Pardon unintended duplications if any.

The savage and the green light

A savage dwelling on a desert island sits in a grass hut entirely filled by green light of wavelength 50 nanopaces. The savage inquires as to the quantum energy of each photon of green light.

Ans: 2 eevee

[If it were blue light with wavelength 40 nanopaces, then the quantum energy would be 2.5 eevee. For convenience assume these are vacuum angular wavelengths---those in air would be scarcely different. The energy multiplied by the angular wavelength is always equal to hbar x c, which in TM units is 100 nanopace eevee.

In metric the same wavelength is 80.9 nanometer, and one could divide 299792458 meters per second by 80.9 nanometer to get 3.70...E15 per second and multiply by h-bar (6.582..E-16 eV second) to get 2.4 eV.]

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The baron and his farmers

A feudal lord is subjecting his farmers to the rack to encourage them to adopt the metric system. The tension at which farmers snap is 1000 oc. On the other hand the elasticity of a farmer is 0.3 millipace per oc. That is to say applying an oc of tension to a farmer makes him stretch a distance of 0.3 millipace. How far does each farmer stretch before snapping?

Ans: 1000 oc times 0.3 millipace per oc is 0.3 pace.

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The scientists and the bumpercar

Two scientists have acquired a bumper-car which they proceed to ram at top speed into the side of the metric system. The vehicle including passengers has a mass of 40 talents and its top speed is 0.3 miles a minute ( 20 mph). What energy is delivered upon impact?

Ans: 1/2 × 40 × 0.3^2 = 1.8 ocmile.

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Henry Kissinger on the White House steps

The well-known diplomat and national security advisor Kissinger had a mass of 5 talents. While fleeing from reporters he once ascended a flight of stairs with a vertical speed of one hundredth of a mile per minute (2/3 mph). What was the trusted advisor's power output on that occasion?

Ans: We multiply his mass by the acceleration of gravity, 17.6 miles per sq.minute, to find the force of his weight, which is 5×17.6 or 88 oc. Ascending at 0.01 mile per minute, his power output is 0.88 ocmile per minute, or 0.88 ponies.

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The ape in pursuit of sport

A Barbary ape pursues a pro-metric lobbyist through the jungle by means of vines. He is swinging on a vine 7 paces long and about to overtake the fleeing lobbyist. How long does a one-way swing of this vine take?

Ans: One radian of swing takes the square root of 0.007/17.6, or 0.02 minutes. A full one-way swing of pi radians takes pi times 0.02 minutes.

The Harley rider

A motorcyclist in a silver-studded black leather jacket and hand-tooled cowboy boots is suddenly seized by beings from another planet and totally converted into energy. The mass of the motorcyclist is four talents, into how much energy is he converted?

Ans: The speed of light is E7 miles a minute (ten million) so the motorcyclist is converted into 4 × E14 ocmiles. (400 trillion).

The corresponding metric mass is 87 kilo and the corresponding metric solution is 87 x 299792458^2 joules.

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Robin Hood

Robin Hood leaps out of a tree and lands on the Sheriff of Nottingham. How much energy is delivered by the impact? The famed outlaw's mass is four talents and the branch from which he leaps is two paces above the sheriff.

Ans. 4 x 17.6 x 0.002 = 0.14 ocmiles.

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The savage and the antenna

A savage on a desert isle wishes to stretch an antenna-wire between two palm trees so that he can listen to a shortwave broadcast of the Rolling Stones. The proper separation between the trees is half the (cyclic) wavelength of the incoming signal which has a frequency of a billion cycles per minute.

Ans: divide E7 miles a minute by E9 cycles a minute to get E-2 mile. A hundredth of a mile is 10 paces, the cyclic wavelength of the signal. The separation between trees should be 5 paces.

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The savage and the weight of the sun

A savage living on a desert isle consults an almanac and learns that the orbit of the earth is nearly circular with an average speed of one thousand miles per minute. The savage wishes to know how much a copy of the sun would weigh if placed at the same distance from the sun that the earth is now.

Ans: The speed is E3 miles a minute. Raise the speed to fourth (E12) and divide by G (E-15) The weight of the sun at this distance would be E27 oc.

Metric solution as a check: raise 30 000 m/s to the fourth (81 E16) and divide by G (6.673E-11). Gives the same force as answer namely 12.1E27 newtons.

ALADDIN AND THE MAGIC UNDERPANTS

Aladdin was a foolish, obstinate boy. One day a wicked sex fetishist, pretending to be the lad's uncle, bade him go down into a dark cave to retrieve some lady's underpants. These were lustrous and smooth as nylon.

Aladdin fetched the underpants and, on returning to the mouth of the cave, refused to hand over the intimate garment until safely out. So the wicked fetishist shut him in the cave and went off to Africa.

Sobbing in terror, the abandoned youth happened to rub the underpants and two Genii appeared offering to grant wishes and perform tasks.

With the aid of the Genii, Aladdin married Badroulboudour, the Sultan's daughter, and had a splendid palace of a million talents constructed for them to live in.

The fetishist, hearing of this, returned from Africa and appeared in rags at the door of the palace offering new undergarments in exchange for old. Aladdin happened to be out of the palace and Badroulboudour, thinking it was a good deal, swapped the magic underpants for some modish new ones made to metric measurements.

Cackling fiendishly, the evil fetishist rubbed the underpants and had the Djinn put the palace on a mile-high mountaintop in Africa.

HOW MUCH WORK was performed by the Genii in raising the million talent palace by one mile?

Ans: One talent weighs 17.6 oc in normal gravity.
Therefore 17.6 million ocmiles.

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HOW A TROLL ATE RALF'S LEG

An active troll requires 1000 ocmiles a day of food energy.

You may recognize that an ocmile is 4.7 food Calories, so this means in conventional terms that the troll's diet contains 4700 Calories a day.

In mechanical terms 1000 ocmile of energy corresponds to pulling a sled for 100 miles over terrain where sleds require 10 oc (27 pound) force to move.

Lean meat contains 10 ocmiles of food energy per oz. So the active troll fed lean meat expects 100 ounces a day.

However the caloric content of fat is much higher---30 per oz. The troll will be satisfied with a mere 33 ounces of fat.

One time Ralf was journeying across the Arctic regions and a troll offered to pull his sled.

Ralf was only too happy to have the troll pull his sled and he relaxed on top of the pile of walrus skins while the troll applied himself to pulling.

However when they were still 3 days from their destination they ran out of blubber to feed the troll and Ralf had to saw off his leg below the knee.

If Ralf's leg had been lean the troll would have required 15 pounds (these are T-M ounces, one thousand to the talent, so 300 oz is 15 pounds). But fortunately his leg was fat so the troll was content with the calf and foot.