Interpreting the Work Equation

Do stairs do work on you when you run up them?

If you are thinking of work as “force times distance” it seems like they might. After all, the stair are pushing you upward and your body is moving upward and forward. But hold on, work is a transfer of energy. The stairs are not transferring energy to you, you are transforming chemical energy into kinetic energy. The stairs don’t get tired… you do. So how can this be consistent with the equation for work, ? The resolution comes in the displacement. The displacement in the work equation is not the displacement of your center of mass. The displacement that matters for work is the displacement of the locus of the force interaction. In this case, it is literally where the stair meets the sole of your shoe. Your body may be moving upward and forward but when your shoe makes contact with the stair that point of contact does not move upward. Therefore, the stair does not do work and does not transfer energy to you.