Unformatted text preview: ile
2
Density = 1.0 lbs /in
Volume = 1 in3 (1 in x 1 in x 1 in)
2
Modulus of Elasticity = 1.0 lb/in
Poisson's Ratio = 0.30
Air Resistance (Viscous Damping)
Alpha Damping Used, Alpha = 1.0 Loading
The acceleration due to gravity is
ay = 386.4 in/s2 in the ydirection.
The initial velocity in the xdirection is Vxi = 100 in/s2, and the initial
velocity in the ydirection is Vyi =
500 in/s2. Analysis Assumptions and Modeling Notes
The acceleration due to gravity is ay = 386.4 in/s2 in the ydirection. The initial velocity in the xdirection is Vxi =
100 in/s2, and the initial velocity in the ydirection is Vyi = 500 in/s2.
The material properties have no effect on the results of interest, so they are selected arbitrarily. As outlined in J.
B. Marion, S. T. Thornton, Classical Dynamics of Particles & Systems, the force due to the air resistance is assumed
to be proportional to the mass, m, and the velocity, v, according to: f air = − k m v
where k is a constant of proportionality. If the initial projectile velocity in the xdirection is U, the initial projectile
velocity in the ydirection (vertical) is V, and the acceleration due to gravity is g, then the x and ydirection projectile
displacements are given by: x= gt
kV + g
U
(1 − exp ( − kt )) ; y = −
+
( 1 − exp( − kt ) )
k
k
k2 For a projectile fired from the ground, the total travel time, T, before returning to the ground, is given by the
transcendental equation: T= kV + g
( 1 − exp ( − kT ) )
gk In thi...
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 Spring '09
 kulasinghe
 The Land, ........., Test Case

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