A comparative study of two methods of determining the Young’s modulus of the material of a cantilever bar by smartphone photography

Abstract In this paper we have determined the Young’s modulus of a cantilever bar by suspending different loads at its free end and finding the depressions due to the load. The depressions being small, we have determined them by taking photographs of the bent bar by a smartphone. We have used two methods for this. In the first method we determine the depressions with respect to a fixed mark on a vertical ruler kept by the side of the bar. The distance between the mark and a red spot at the end of the cantilever bar is measured from the photograph. With freely available software from the internet we can find the width of the real image on the sensor of the digital camera precisely in terms of pixel with micron level accuracy. Applying laws of geometrical optics we can find the depressions in real space. We discuss a second method where we measure the depressions from a horizontal laser beam running above the cantilever bar as reference level.This method gives better results of the Young’s modulus.