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There is considerable interest in measuring, with nanoscale spatial resolution, the physical properties of lipid membranes because of their role in the physiology of living systems. Due to its ability to nondestructively image surfaces in solution, tapping mode atomic force microscopy (TMAFM) has proven to be a useful technique for imaging lipid membranes. However, further information concerning the mechanical properties of surfaces is contained within the time-resolved tip/sample force interactions. The tapping forces can be recovered by taking the second derivative of the cantilever deflection signal and scaling by the effective mass of the cantilever; this technique is referred to as scanning probe acceleration microscopy. Herein, we describe how the maximum and minimum tapping forces change with surface mechanical properties. Furthermore, we demonstrate how these changes can be used to measure mechanical changes in lipid membranes containing cholesterol.