The relation between the tension T and the steady shortening velocity v in a muscle is given by the Hill equation:
(T + a)(v + b) = (T0 + a)b
where a and b are positive constants and T0 is the isometric tension, i.e., the tension in the muscle when v = 0. The maximum shortening velocity occurs when T = 0.
(a) Using symbolic operations create the Hill equation as a symbolic expression. Then use subs to substitute T = 0, and finally solve for v to show that vmax = (bT0)/a.
(b) Use vmax from part (a) to eliminate the constant b from the Hill equation, and show that v
= a(T0 - T)/T0(T + a) Vmax.