Structural Maintenance of Chromosomes (SMC) complexes play essential roles in genome organization across all domains of life. To determine how the activities of these large (≈50 nm) complexes are controlled by ATP binding and hydrolysis, we developed a molecular dynamics model that accounts for conformational motions of the SMC and DNA. The model combines DNA loop capture with an ATP-induced 'power stroke' to translocate the SMC complex along DNA. This process is sensitive to DNA tension: at low tension (0.1 pN), the model makes loop-capture steps of average 60 nm and up to 200 nm along DNA (larger than the complex itself), while at higher tension, a distinct inchworm-like translocation mode appears. By tethering DNA to an experimentally-observed additional binding site ('safety belt'), the model SMC complex can perform loop extrusion (LE). The dependence of LE on DNA tension is distinct for fixed DNA tension vs. fixed DNA end points: LE reversal occurs above 0.5 pN for fixed tension, while LE stalling without reversal occurs at about 2 pN for fixed end points. Our model matches recent experimental results for condensin and cohesin, and makes testable predictions for how specific structural variations affect SMC function.