= Solution
The <atomic force microscope> measures the <cantilever> deflection $d$, converted to normal <force> by $F=k_cd$ after <calibration>. On approach, the <force> is initially almost zero, then attractive; a sufficiently steep attractive <force> gradient causes <jump-to-contact>. After contact, further approach bends the <cantilever> and indents the sample, giving a rising repulsive branch. With tip-surface separation increasing to the right, approach proceeds from right to left. The instability occurs when the magnitude of the attractive <force> gradient exceeds the <cantilever> stiffness. The contact-branch slope depends on both <cantilever> and sample compliance.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2020/paper-1-afm-force.png]
{title=Approach force curve and the additional retraction information used in mechanical mapping}
{source=paper-1-afm-force.py}
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