Problem 323. Mechanics 1

Created by Matt Fig

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>I thought I would make a mechanics problem for all those physics lovers out there.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>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&lt;x2&lt;(R1+R2) and sqrt((R1+R2)^2-x2^2)&lt;y2. Gravity acts in the negative y direction with constant g = 9.8 in some consistent unit system.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>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:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[[V1,V2] = balldrop_puzz(M1,M2,R1,R2,x2,y2)\n\nV1 = [-10.8362631979321 0]\nV2 = [5.41813159896603 2.66024980473149]]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

147 Solutions
23 Solvers

Last Solution submitted on Mar 10, 2023

Last 200 Solutions

Problem Comments

5 Comments

5 Comments

Show 2 older comments

@bmtran (Bryant Tran) on 16 Feb 2012

if you didn't already have a master's in mechanical engineering, i'd be concerned this was your homework problem.

Matt Fig on 16 Feb 2012

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!

Tom on 16 Feb 2012

I assuming that you're neglecting any rotation caused by grazing collisions.

Matt Fig on 16 Feb 2012

@Tom, yes that is true. There is no friction.

Rafael S.T. Vieira on 15 Jul 2020

The tip is coefficient of restitution (COR); and imagining that B1 is a pendulum may help.

Solution Comments

Solution 43427

3 Comments

3 Comments

Matt Fig on 17 Feb 2012

Well done, sir!

Tim on 17 Feb 2012

Thank you.

Anuka Mithara Karunanayake on 9 Jun 2020

????????????????

Problem Recent Solvers23

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 323. Mechanics 1

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers23

Suggested Problems

More from this Author6

Problem Tags

Community Treasure Hunt

Problem 323. Mechanics 1

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers23

Suggested Problems

More from this Author6

Problem Tags

Community Treasure Hunt

Players