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At position (1), the AFM probe is far from the surface, with approximately zero force. At (2), attractive interactions bend the AFM cantilever toward the surface; when the attractive force gradient exceeds the cantilever spring constant, the equilibrium becomes unstable and jump-to-contact occurs. Position (3) is on the mechanical-contact branch: changes in imposed height largely bend the AFM cantilever and, for a compliant specimen, indent the sample. This branch can include compressive contact and adhesive contact under tension; contact does not itself imply a positive force at every point. At (4), during withdrawal the tip remains attached and pulls the AFM cantilever downward until the pull-off force is reached and it detaches. Approach and retraction follow different paths because adhesion creates a hysteretic contact. The numbered points identify stages on the source curve, not four extra question parts.

The atomic force microscope measures the cantilever deflection $d$, converted to normal force by $F=k_{c}d$ 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.