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Physics I Lab Manual 2011 90 - the velocity and...

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EXPERIMENT 13. NUMERICAL ANALYSIS Figure 13.1: Free body diagram for a falling baseball Newtons 2nd law in the vertical direction is written as: F d - mg = ma with F d = 0 . 22 d 2 v 2 . As the ball falls, the velocity increases until the drag force balances the gravitational force so that the net force is zero. To predict the motion of the ball, we need to calculate the resultant force and velocity produced by the drag using simple step functions over a small time interval in which the acceleration is assumed constant. New values of position and velocity are calculated from previous values of velocity and acceleration. The repetitive arithmetic in these step equations is just what computers were developed for. These equations use the simplest estimate for
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Unformatted text preview: the velocity and acceleration in each interval. The larger the interval the less accurate the estimate over this interval is. Our text book develops slightly more detailed expressions, but the core concept for this and all the more sophisticated treatments is the same: if we know the forces, Newtons second law lets us predict the motion. Calculations 1. Air Resistance on a Baseball . A thrown ball will encounter an air resistance force proportional to the square of its diameter d and its speed v . This drag force is given by F d ( v ) = ± . 22 kg m 3 ² d 2 v 2 80...
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