Design of a micro-machined cantilever apparatus suitable for testing Modified Newtonian Dynamics

Abstract

Micro-cantilevers have been used for Atomic Force Microscopy to obtain topographic images of surfaces. The resolution of these images allows for individual atoms to be resolved. In this work micro-cantilevers were studied to determine their noise spectrum. A theoretical model was derived using the Euler-Bernoulli beam equation, hydrodynamics and thermodynamics to ascertain the expected power spectral density of a micro-cantilever in a fluid due to thermal energy. Experimental data was collected with a lock-in amplifier to measure noise vs frequency to compare with the theoretical model. The data was used to determine the expected uncertainty of measurements due to noise to determine if measurements can be made in the MOND regime. These results will be used to determine the viability of using a micro-cantilever for an Earth based experiment to test MOND.