As we all know, Justin Timberlake is a multitalented sensation who has graced our TVs and radios with his comeback in recent years. So great is his entertainment value that Netflix has deemed him worthy of a documentary following his most recent tour, the 20/20 Experience. While most artists have a vast wardrobe that they rotate through for shows, ever-classy JT's perpetual suit-and-tie look services him beyond just making the ladies swoon. He is able to harness the power of the smooth-soled dress shoe in ways that many of us at various weddings, bar mitzvahs, etc. have fallen prey to on the dance floor. Anyway, there's some science involved.
Lee et al. document the coefficient of kinetic friction of dress shoes on a treadmill to be 0.20 (surprisingly, there aren't many resources documenting shoe friction. Go figure.) Since treadmills are theoretically made to aid running, let's assume that this coefficient is 0.05 higher than that of dress shoes on a stage. Let's also assume that our superstar doesn't have custom-made shoes specifically for dancing (he totally does). Most of Justin's moves involve sliding in some capacity. As he slides forward on one foot (see picture below. Ok enough staring, we have physics to do), his initial acceleration is in the forward direction from the push off his other foot, and friction is resisting the movement. If we google his weight, we find it is 76kg, which we can use to find the normal force.
The only force acting on his movement after his pushing foot leaves the ground is the force of friction. His acceleration is negative since he is slowing down. We see the frictional force (76*9.81*.15) is equal to 110 N. Therefore, using kinematics equations, he can calculate the force he needs to push off with in order to travel a certain distance in a certain amount of beats. He also does some really cool spins and jumps and moves on his toes but that's physics for another day.