''Diagonalization'' of a compound Atwood machine

Journal Article · Mon Jun 01 00:00:00 EDT 1987 · Am. J. Phys.; (United States)

DOI:https://doi.org/10.1119/1.15105· OSTI ID:6628807

Crawford, F S

We consider a simple Atwood machine consisting of a massless frictionless pulley no. 0 supporting two masses m/sub 1/ and m/sub 2/ connected by a massless flexible string. We show that the string that supports massless pulley no. 0 ''thinks'' it is simply supporting a mass m/sub 0/, with m/sub 0/ = 4m/sub 1/m/sub 2//(m/sub 1/+m/sub 2/). This result, together with Einstein's equivalence principle, allows us to solve easily those compound Atwood machines created by replacing one or both of m/sub 1/ and m/sub 2/ in machine no. 0 by an Atwood machine. We may then replacing the masses in these new machines by machines, etc. The complete solution can be written down immediately, without solving simultaneous equations. Finally we give the effective mass of an Atwood machine whose pulley has nonzero mass and moment of inertia.

• Research Organization: Lawrence Berkeley Laboratory and Physics Department, University of California, Berkeley, California 94720
• OSTI ID: 6628807
• Journal Information: Am. J. Phys.; (United States), Vol. 55:6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MECHANICAL STRUCTURES
EQUIVALENCE PRINCIPLE
ACCELERATION
MASS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics