TimeOfFlightDiameterMeasurementHW

# TimeOfFlightDiameterMeasurementHW - =-= = =(4 29 29 29 29...

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ABE 425 Time of Flight Diameter measurement under constant acceleration 4 t 3 t 2 t D D b b 1 t Time (s) Distance (m) ( 29 1 t x ( 29 2 t x ( 29 3 t x ( 29 4 t x p t f t Under the assumption of constant velocity, the time it takes an object to move through the distance b from layer 1 to layer 2 is f t . Therefore the velocity is simply: f b v t = (1) The diameter of the object is represented by the time it takes to move the object through one of the light layers times the velocity of the object or: p p f t D v t b t = ∆ = (2) Assume a contant velocity 0 v : The equation of motion of the particles is now: ( 29 0 0 x t x v t = + (3) Now we can write according to the figure:

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ABE 425 Time of Flight Diameter measurement under constant acceleration ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 0 1 0 2 0 2 0 2 1 0 2 0 0 1 0 0 2 1 0 0 0 f f f x t v t x x t v t x x t x t b v t x v t x v t t v t b v t b v t = + = + - = = + -
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Unformatted text preview: + =-= = = (4) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 0 3 2 0 2 3 1 0 3 0 1 3 1 p p p p f f x t v t x x t v t x x t x t D v t x v t x v t t v t D v t t b D t b t t = + = +-= = +-+ =-= = = = (5) ABE 425 Time of Flight Diameter measurement under constant acceleration HW: Derive the equations for the Diameter if the particle does not have a constant velocity, but a constant acceleration. This means that the general equation of motion becomes: 4 t 3 t 2 t D D b b 1 t Time (s) Distance (m) ( 29 1 t x ( 29 2 t x ( 29 3 t x ( 29 4 t x p t f t ( 29 2 1 2 x t x v t at = + + (6)...
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## This note was uploaded on 11/30/2010 for the course ABE ABE425 taught by Professor Tonygrift during the Spring '10 term at University of Illinois, Urbana Champaign.

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TimeOfFlightDiameterMeasurementHW - =-= = =(4 29 29 29 29...

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