We can use an atomic force microscope (afm) to measure forces exerted on a molecule attached to a surface (and hence to measure the spring-like force of the molecule pulling back on the afm tip) as a function of molecular length. however, when we measure forces at the microscopic scale, one problem is that you have to attach the molecules of interest using stretchy bonds of some sort. let? s model that and solve for a result.

instead of an afm tip pulling on the springy-molecule, let? s use a mass applying a weight to a spring. let? s replace the bond attaching the molecule to the surface with a different spring in between the first spring and the ceiling. let? s compute what happens and see what lessons emerge.

a) we have two springs suspended as shown at the right. the top spring (spring constant 3k) is attached to the ceiling and the bottom spring (spring constant k) is attached to a mass, m. assume the entire system is at rest. draw the free body diagram for each spring and the mass.

image for we can use an atomic force microscope (afm) to measure forces exerted on a molecule attached to a surface (and
b) find the extension of each spring in terms of m, k and g.

c) comment on why this result is relevant to our experimental problem, and, based on your result from part b), what properties you? d like the bond attaching the molecule to the afm tip and surface to have.