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Density = 1.0 lb-s /in
Volume = 1 in3 (1 in x 1 in x 1 in)
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 y-direction.
The initial velocity in the x-direction is Vxi = 100 in/s2, and the initial
velocity in the y-direction is Vyi =
500 in/s2. Analysis Assumptions and Modeling Notes
The acceleration due to gravity is ay = 386.4 in/s2 in the y-direction. The initial velocity in the x-direction is Vxi =
100 in/s2, and the initial velocity in the y-direction 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 x-direction is U, the initial projectile
velocity in the y-direction (vertical) is V, and the acceleration due to gravity is g, then the x and y-direction projectile
displacements are given by: x= gt
kV + g
(1 − exp ( − kt )) ; y = −
( 1 − exp( − kt ) )
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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This note was uploaded on 12/09/2010 for the course DEPARTMENT E301 taught by Professor Kulasinghe during the Spring '09 term at University of Peradeniya.
- Spring '09
- The Land