Cancer cells become mobile by remodelling their cytoskeleton to form migratory structures. This transformation is dominated by actin assembly and disassembly (polymerisation and depolymerisation) in the cytoplasm. Synthesis of filamentous actin produces a force at the leading edge that pushes the plasma membrane forward. We describe an assay to measure the restoring force of the membrane in response to forces generated within the cytoplasm adjacent to the membrane. A laser trap is used to form a long membrane nanotube from a living cell and to measure the axial membrane force at the end of the tube. When the tube, resembling a filopodium, is formed and in a relaxed state the axial membrane force exhibits a positive stationary value. This value reflects the influence of the cytoskeleton that acts to pull the tube back to the cell. A dynamic sawtooth force that rides upon the stationary value is also observed. This force is sensitive to a toxin that affects actin assembly and disassembly, but not affected by agents that influence microtubules and myosin light chain kinase. We deduce from the magnitude and characteristics of dynamic force measurements that it originates from depolymerisation and polymerisation of F-actin. The on- and off-rates, the number of working filaments, and the force per filament (2.5 pN) are determined. We suggest the force-dependent transitions are thermodynamically uncoupled as both the on- and off-rates decrease exponentially with a compressive load. We propose kinetic schemes that require attachment of actin filaments to the membrane during depolymerisation. This demonstrates that actin kinetics can be monitored in a living cell by measuring force at the membrane, and used to probe the mobility of cells including cancer cells.