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Full-Text Articles in Physics
The Role Of Friction In The Static Equilibrium Of A Fixed Ladder: Theoretical Analysis And Experimental Test, Mark P. Silverman
The Role Of Friction In The Static Equilibrium Of A Fixed Ladder: Theoretical Analysis And Experimental Test, Mark P. Silverman
Faculty Scholarship
In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on …
Reaction Forces On A Fixed Ladder In Static Equilibrium: Analysis And Definitive Experimental Test Of The Ladder Problem, Mark P. Silverman
Reaction Forces On A Fixed Ladder In Static Equilibrium: Analysis And Definitive Experimental Test Of The Ladder Problem, Mark P. Silverman
Faculty Scholarship
The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is that the problem is statically indeterminate and therefore requires complementary information to obtain a unique solution. This paper reports 1) a comprehensive theoretical analysis of the three fundamental models based on treating the ladder as a single Euler-Bernoulli beam, and 2) a detailed experimental investigation of the forces of reaction as a function of applied load and location of load. In contrast to previous untested proposals …
Bending Of A Tapered Rod: Modern Application And Experimental Test Of Elastica Theory, Mark P. Silverman, Joseph Farrah
Bending Of A Tapered Rod: Modern Application And Experimental Test Of Elastica Theory, Mark P. Silverman, Joseph Farrah
Faculty Scholarship
A tapered rod mounted at one end (base) and subject to a normal force at the other end (tip) is a fundamental structure of continuum mechanics that occurs widely at all size scales from radio towers to fishing rods to micro-electromechanical sensors. Although the bending of a uniform rod is well studied and gives rise to mathematical shapes described by elliptic integrals, no exact closed form solution to the nonlinear differential equations of static equilibrium is known for the deflection of a tapered rod. We report in this paper a comprehensive numerical analysis and experimental test of the exact theory …