Pyramid Science

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Friday, June 11, 2010

Momentum And Kinetic Energy

The momentum (p) of an object is given by:

p = mv 

where m is the mass of the object and v is its (constant) velocity. An object moving at a non-constant speed will either be accelerating or decelerating in which case the kinetic energy must be considered:

KE = ½mv²

A small object travelling at high speed has a greater energy than a larger, slower-moving, object. Consider a 1kg mass moving at 2m/s and one with half the mass (500g), but twice the velocity (4m/s). The KE of the slower-moving heavier object is 2kg/m² (0.5 x 4) and the faster, but lighter object has KE4kg/m² (0.25 x 16). So, fast and light has a greater potential for damage than slow and heavy. The momentum will increase with an increase in the mass of the object. It's why a moderately fast-moving train can suffer a mixture of damage: impacting on trees will cause the tree to break with some impact damage, yet an immovable rock will cause total devastation. The rock will remain undamaged. If the impact area consists of trees and rocks, different rates of momentum loss will occur. The train will slow and the overall momentum will be reduced. Eventually, impacting on objects and friction forces (the train has been derailed) will result in the velocity becoming zero: completely stopped. The passengers will suffer both serious and fatal consequences as they themselves only reduce their velocity (initially the speed of the train) by impacting on objects within the train: other passengers, walls, windows, doors.

The momentum (kg/m/s) of a 50 tonnes Chieftain battle tank travelling off-road at 30km/h will easily pass through a brick house wall when a 2 ton car will not. Yet the lighter and potentially faster car could acquire the KE to destroy the wall and the car may survive relatively undamaged. The physics of speed and momentum appear complex if only the result is considered, but outcomes are predictable. The resistance of the brick wall could be more than sufficient to overcome the intrinsic momentum of the car, but not the tank. If the heavy tank impacted on a relatively immovable object, like a large rock wall (mountainside), the front of the tank will come to an abrupt stop, but the rest of the tank will continue moving crushing what is ahead of it: the front part of the same tank. An aircraft that weighs considerably more, crashing into the ground at 600km/h, will be totally crushed, though unless hitting a mountain, a small impact crater or dent would be visible.
  • Movement in water involves hydrostatics and some curious observations can be noted, but it is not thixotropic (yielding to forces created by pressure). A very slow-moving paddle does not have much of an effect when moving in water. Too fast and a similar outcome will be observed: the paddle will pass through water with little effect. There is an optimum speed that will produce the best result.


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