By Robert Aebi
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19) The trip time is then, T = π/ωo , which for the Earth is 2533 sec, or about 42 minutes, independent of the trip distance. The script which was written to cover this problem appears in “cm subway2”. 24. Who says there is no free lunch? 23: Printout for the user supplied distance along the subway showing the subway depth, surface distance, and travel time. However, the velocity of the trip increases with the distance and the heat encountered in a “deep” trip might be a bit impractical. Still, the study of the use of the properties of the inverse square law for gravity is amusing.
The damped frequency in the absence of damping and driving terms is ωo2 = k/m and the motion is oscillatory, x ∼ e±iωo t . This second order equation needs initial values for position and velocity to be defined in order for the solution to be fully determined. In this exercise, supplied by the script “cm osc” an initial displacement is supplied equal to A and the initial velocity is defined to be zero. There are three cases which are considered; no damping, no driving term, then damped motion without driving forces, and then damped and driven motion.
In this way, an intuition is built up as regards the kinematics of scattering. 14, a frame of the movie for the case of M = 1 is shown. In this case, the projectile can transfer all its velocity to the target, which is familiar in billiards. Note that the angle between the scattered projectile and the recoiling target in this equal mass case is always ninety degrees. 14: Scattering of a projectile and the recoil momentum and angle for the case of equal target and projectile mass. This is a snapshot of a movie covering several scattering angles.