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7.8. END OF CHAPTER PROBLEMS
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(17a) Write a script that generates N random masses between minM and maxM
kg and N random velocity vectors (x, y, z components) with component
magnitudes between minV and maxV. Print out the individual kinetic energies and the total kinetic energy of the eight particles. Every time you
run the script, it should generate new random masses and velocities. Test
the script with N=8, minM=1, maxM=10 kg, minV=-100 m/s, maxV=100
m/s.
(17b) Extend the script from part a to calculate the velocity, speed and kinetic
energy of the center of mass of the 8-body system.
(17c) Extend the script further to calculate the kinetic energy of the masses
relative to the center of mass. The part b and c results should sum to the
energy from part a. Your script should demonstrate that this is so. Run the
script 10 times and thus demonstrate numerically that total kinetic energy
breaks into the kinetic energy of the center of mass + the kinetic energy
relative to the center of mass.
(18) Write a Matlab function defined as follows:
1 f u n c t i o n [ R]= s c h a r z c h i l d R a d i u s (M)
2 %M [ k g ] : M a s s o f l a r g e b o d y
3 %R [ m ] :
S c h w a r z c h i l d Radius o f body
Test your function with a script that prints out the Schwarzchild radius of
the Earth, the Sun, and your own body. The Schwarzchild radius is defined
in problem 6.