Problem 323. Mechanics 1
I thought I would make a mechanics problem for all those physics lovers out there.
Imagine two solid, rigid spheres B1 and B2 with radius R1 and R2 and mass M1 and M2. B1 initially has its center of mass at the origin and is confined to always move along the x axis. B2 has its center of mass located at coordinates (x2,y2) where 0<x2<(R1+R2) and sqrt((R1+R2)^2-x2^2)<y2. Gravity acts in the negative y direction with constant g = 9.8 in some consistent unit system.
Write a function that returns the velocity of both spheres after B2 is allowed to fall, assuming a lossless collision occurs. Keep in mind that the answers should be two-element row vectors. For example, if R1=1, R2=.25, M1=2, M2=4, x2=.5 and y2=6, then:
[V1,V2] = balldrop_puzz(M1,M2,R1,R2,x2,y2)
V1 = [-10.8362631979321 0] V2 = [5.41813159896603 2.66024980473149]
Solution Stats
Problem Comments
-
6 Comments
if you didn't already have a master's in mechanical engineering, i'd be concerned this was your homework problem.
LOL, bmtran! Just trying to have a little fun with the format. Indeed, it has been so long since I solved this kind of problem that I can only hope I didn't make a mistake that would show up in the test-suite!
I assuming that you're neglecting any rotation caused by grazing collisions.
@Tom, yes that is true. There is no friction.
The tip is coefficient of restitution (COR); and imagining that B1 is a pendulum may help.
after fall, is B2 hitting B1 directly?
Solution Comments
Show commentsProblem Recent Solvers28
Suggested Problems
-
Find state names that start with the letter N
1233 Solvers
-
Reverse the elements of an array
1023 Solvers
-
Calculate the Number of Sign Changes in a Row Vector (No Element Is Zero)
720 Solvers
-
328 Solvers
-
159 Solvers
More from this Author6
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!