Consider the Hill model: (T+a)v= b (T0-T) in which a and b are constants determi

Question

Consider the Hill model: (T+a)v= b (T0-T) in which a and b are constants determined from data; T0 and T represent the tension (or contractile force) in the muscle, T0 represents the tension at zero speed and v is the speed of contraction. Find the maximum value of the power, P=Tv, with respect to velocity and determine the corresponding tension and speed in terms of a, b and T0. (Hint: recall the definition of a maximum value of a function.) Use the following values obtained for the frog Sartorius muscle a=14.35 g, b=1.03 cm/s, T0= 70.70 g to compute a specific value for the tension and speed at maximum power.

Explanation / Answer

v= b(T0 - T)/ (T+a) put this in expression of P=Tv P= Tb(T0 - T)/ (T+a), to get maximum power differentiate this express; Tb(T0 - T) = (T+a)(b(T0- T)- bTT0 obtain the T, at that Tyou will have maximum power, further you have a,b, T0 values put in the expresion to get answer

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