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

a)
`F=50\ N`

b)
`F'=5\ N`

c)
`v=24\ cm.s^(-1)`

d)
`F`

Step-by-step 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=(20)/(8) =(5)/(2)=2.5 \ cm^2`

a)

Maximum force developed by this muscle:

`F=\sigma* A`

`F=20* 2.5`

`F=50\ N`

b)

Force when the muscles are 10% activated:

`F'=10\%\ of\ F`

`F'=(50)/(10)`

`F'=5\ N`

c)

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

• time taken for the contraction,
  `t=50* 10^(-3)\ s`

Now, the speed of the muscle:

`v=(\Delta l)/(t)`

`v=(0.15* 8)/(50* 10^(-3))`

`v=24\ cm.s^(-1)`

d)

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

`F`

`F`