Hitting Buster above his center of gravity causes his upper body to rotate "backwards," which is equivalent to the lower body rotating "forwards." Thus, the punch actually drives the feet deeper into the socks! (A backward blow, or a hit below the belt, creates a force in the right direction, but the right angle of the heel dampens it. Would it work anyway? Only one way to find out, I suppose.)

The sock-seperating force must, therefore, arise either from a linear acceleration of Buster's leg (i.e. from the "follow-through" of an ideal uppercut) or from torque as the leg is whipped.

In considering the linear case, assume an "ideal" uppercut that transmits all its force along the longitudinal axis of the body. By Newton's second law, the acceleration of the leg and body relative to the sock is given by:

a_body = F_body / m_body.

This is equal in magnitude (opposite in direction) to the acceleration of the sock relative to the leg:

a_sock = F_sock / m_sock.

Thus, considering only magnitudes, |F_body| = |F_sock| * (m_body / m_sock). Since the mass of the body is many, many times more than the mass of the sock, so must the force of the uppercut be many, many times more than the force needed to pull off the sock. Substituting the measured force of static friction on the sock for |F_sock| gives a lower bound for |F_body|.


For the other case (whipping), see my next post.