Question

4. Consider muscle fibers that are 8 cm long and that develop a maximum of 20 N/cm2 force. Consider a muscle that has a volume of 20 cm3 with the fibers aligned with the direction of the tendon (θ=0).
a.) What is the maximum force developed by this muscle? (5 points)
b.) If partial recruitment results in activation of 10% of the muscle fibers (assuming they are all of equal size), how much force could the muscle generate? (5 points)
c.) If the muscle fibers contract 15% of their length in 50 ms under no load, what is the maximum muscle velocity? (5 points)
d.) Suppose the muscle fibers are oriented at 15° relative to the tendon axis, with the same volume of muscle. What is the maximum force delivered to the tendon? What is the maximum velocity? (5 points)

Answer 1

Answer:

a) $F=50\ N$

b) $F'=5\ N$

c) $v=24\ cm.s^{-1}$

d) $F"=48.2963\ N$

Explanation:

Given:

• length of muscle fibers, $l=8\ cm^2$

• maximum stress on each fiber, $\sigma=20\ N.cm^{-2}$

• Volume of muscles, $V=20\ cm^3$

∴Area of the muscle:

• $A=\frac{20}{8} =\frac{5}{2}=2.5 \ cm^2$

a)

Maximum force developed by this muscle:

$F=\sigma\times A$

$F=20\times 2.5$

$F=50\ N$

b)

Force when the muscles are 10% activated:

$F'=10\%\ of\ F$

$F'=\frac{50}{10}$

$F'=5\ N$

c)

• contraction in length of muscle, $\Delta l=15\%\ of\ l$

• time taken for the contraction, $t=50\times 10^{-3}\ s$

Now, the speed of the muscle:

$v=\frac{\Delta l}{t}$

$v=\frac{0.15\times 8}{50\times 10^{-3}}$

$v=24\ cm.s^{-1}$

d)

Maximum force delivered when the muscle fibers are oriented at 15° from the tendons:

$F"=50\ cos\ 15^{\circ}$

$F"=48.2963\ N$