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The Physics of Ancient Roman Technology
Transcript of The Physics of Ancient Roman Technology
1. The weight of block A.
2. The weight of block B on block C.
3. The restoring force of block B's support, block C. The physics of the Roman arch works similarly to the alphabet blocks, except the position of the stones on the arch are slightly different. They are constructed to form a semicircular shape. Horizontal and Vertical Force Components The sum of the vertical components is zero. The sum of the horizontal components is also zero. The horizontal forces are the same for each block since the weight of each block is perpendicular to the ground. The vertical forces increase as you move down the arch. The Amphitheatre The Romans build amphitheatres for performances and gladiator games. The stage is surrounded by ascending seating. Sounds of performances were heard pretty well. Sound limestone seats
sounds with frequencies of 500 Hz and lower were suppressed
virtual pitch The Aqueduct The aqueduct predominantly relies on gravity to function. Because the rate of the water flow relies on gravity, the aqueducts must be build on a very small declining slope, or gradient. 200 million gallons of clean water were brought into Rome per day from miles away during Gaius Octavius's rule (27 BC - 14 AD). The Treadwheel Crane The treadwheel crane was used for lifting heavy objects such as stones for construction. There were three kinds of cranes: trispastos, pentaspastos, and polypastos. maximum load = (# of ropes)(# of pulleys)(# of men)(50 kg) We assume that 50 kg is the maximum effort a man can exert over a long period of time. Example 1: Polypastos (3 ropes)(5 pulleys)(4 men)(50 kg) = 3000 kg The polypastos could lift approximately 3000 kg. Example 2: Pentaspastos (1 rope)(5 pulleys)(2 men)(50 kg) = 500 kg Example 3: Trispastos (1 rope)(3 pulleys)(1 man)(50 kg) = 150 kg Weapons Ballista The ballista was a Roman weapon used to launch large objects at distant objects. It works similarly to a crossbow. As the object is drawn back, the arms are pulled along, creating tension in the torsion springs. The rope then acts as a giant spring to hurl the object towards enemies. Hooke's Law F=-kd Force = -(force constant of the ropes when under tension)(distance arms drawn back) Moving the arms back 2 meters would give about twice the force that moving back the arms 1 meter would do. When force is applied, projectile accelerates to end of ballista, released with velocity v and angle q from the horizontal. where x is length of ballista projectile is accelerated upon Because F=ma and F=-kd, After its release, the projectile motion can be calculated: where R=range and g=acceleration due to gravity Scorpio The scorpio is a weapon similar to the ballista except that is permits only one person for use. Its concept is just like the ballista's. Onager This weapon works like the ballista and the trebuchet. It is the Roman's catapult device that involves the physics of the lever and sling. The onager is powered by gravity or applied force. As it slings, it creates a parabolic shape. Class 1 Lever v = gt Lower frequencies are harder to absorb because of their longer wavelengths. The End