{"id":154,"date":"2023-02-14T09:16:22","date_gmt":"2023-02-14T14:16:22","guid":{"rendered":"https:\/\/commons.princeton.edu\/1954-tiger-cub\/?page_id=154"},"modified":"2023-04-18T05:48:45","modified_gmt":"2023-04-18T09:48:45","slug":"science","status":"publish","type":"page","link":"https:\/\/commons.princeton.edu\/1954-tiger-cub\/science\/","title":{"rendered":"Science"},"content":{"rendered":"

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Thermal expansion:<\/p>\n

The coefficient of thermal expansion of a rod is equal to the ((change in length) \/ (length)) for a change in temperature in a given unit (Centigrade or Fahrenheit, for example)<\/p>\n

The coefficient of thermal expansion for aluminum is about 22ppm (parts per million) \/ degree C or 12 ppm \/ degree F<\/p>\n

A design question: What is the allowable temperature rise for a 5″ long aluminum pushrod if the Tappet clearance is 0.010″ ?<\/p>\n

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Principle of Virtual Work:<\/p>\n

WORK IN = WORK OUT;\u00a0 Work = Force x Distance<\/p>\n

A 1\/4-20 jack screw is used to lift a weight; it is turned CCW with 1 ft-lb of torque.\u00a0 What is the vertical force?<\/p>\n

1 ft-lb torque could be produced by turning the screw with a 6″ wrench with 2 lb Force applied to the end of the wrench – one rotation would be 12 pi inch travel of the end of the wrench – so the WORK IN would be 2 lb times 12pi inches or 75.4 inch-lb; the screw rotated one revolution CCW would move 1\/20th of an inch upward, so the WORK out would be the LIFTING FORCE x 0.05″; since the WORK IN = WORK OUT, the LIFTING FORCE would be 75.4 inch-lb \/ 0.05 inch = 1508 lb.<\/p>\n

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Coulomb Friction – also know as Stick-Slip Friction:<\/p>\n

Horizontal Force = (Coefficient of Friction) x (Normal Force)<\/p>\n

The coefficient of friction for rubber on asphalt is about 1.\u00a0 The motorcycle weighs 200 pounds.\u00a0 The rider weighs 200 pounds.\u00a0 The distance between the rear axle and the ground is 1 foot.\u00a0 How much torque on the rear wheel will cause the rear wheel to slip?\u00a0 What is the maximum force accelerating the motorcycle forward?<\/p>\n

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Gears, and Chain-and-Sprocket – decreases speed, increases torque<\/p>\n

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Top speed of crank = 6000 RPM = 100 Revolutions per second<\/p>\n

Rear wheel radius (axle to ground) = 1 foot<\/p>\n

Wheel circumference = 6.28 feet<\/p>\n

Top motorcycle speed in top gear is (100\/6.84)*6.28 = 91.8 feet per second or about 63 mph<\/p>\n

Coefficient of friction for rubber tires on asphalt is about 1 – normal load is about 200 lbs<\/p>\n

So, the torque on the rear wheel where the tire starts to slip is about 200 ft-lbs.<\/p>\n

In the lowest gear the overall gear ratio (engine crank to rear wheel) is 20.3.<\/p>\n

So, the torque on the crank that produces 200 ft-lbs is 200\/20.3 = 9.85 ft-lbs.<\/p>\n

Where does the 6.84 come from in the table above?\u00a0 It is (48\/19)*(46\/17) = 6.836.<\/p>\n

That is, 6.836 is the turns ratio of the crank reduced by primary chain linking Engine to the Clutch times the turns ratio of Gearbox reduced by the drive chain linking the Gearbox to the Rear Wheel.<\/p>\n

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Stick-Slip Friction:<\/p>\n

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Gravitational Lensing (curvature of spacetime)<\/p>\n

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Einstein Cross – Multiple images of same Quasar by gravitational lensing due to galaxy in line of sight.<\/p>\n