Chapter 11, Problem 13P

The mechanical power output P in a contracting muscle is given by:

$P=TV=\frac{kv{T}_0(1-\frac{v}{v_{\max }})}{k+\frac{v}{v_{\max }}}$

where T is the muscle tension, v is the shortening velocity (max of v_max), T₀is the isometric tension (i.e., tension at zero velocity), and k is a nondimensional constant that ranges between 0.15 and 0.25 for most muscles. The equation can be written in nondimensional form:

$p=\frac{ku(1-u)}{k-u}$

where p=(Tv)/(T₀v_max) ,and u=v/v_max. Consider the case k = 0.25.

(a) Plot p versus u for $0\le u\le 1$ .

(b) Use diftirentiation to find the value of u where p is maximum.

(c) Find the maximum value of p.