Chapter 11, Problem 9P

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 T₀is 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 v_max=bT₀)/a. (b) Use v_max from part (a) to eliminate the constant b from the Hill equation, and show that $v=\frac{a(T_0-T)}{T(T+a)}{v}_{\max }$ .