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3 Mechanical Aspects of Biosystems
Determine the stress on the discs when the woman stands. During the day, after
4 h, the strain of the cervical region has become 2%, which is 60% of its longperiod strain. The spine expands back to its original length during the night when the
body is prone. There is little compression of the vertebrae between the intervertebral
discs.
Fit this data to a Kelvin-Voigt model of the intervertebral discs.
Plot the predicted strain as a function of time (in hours) during the day.
3.14 A 45 kg woman jumps from a height of 2.5 m to a solid floor. In an attempt
to minimize the likelihood of injury, she lands on the ball of her feet (the pads just
behind her toes) with her knees bent. What average force is needed on her feet to
stop her fall if her center-of-gravity after touching the floor drops 80 cm before she
stops? If the horizontal distance from the ball of her foot to her talus (where her tibia
exerts its force) is 15 cm, and from talus back to the Achilles tendon is 3.6 cm, what
average force does the Achilles tendon suffer during the stopping time?
3.15 The bone around your teeth behaves somewhat like a Maxwell viscoelastic
material. When stressed by the pressure of a tooth, the bone, over time, moves to
relieve the stress. Suppose we find that the stress on the bone next to a tooth drops
linearly with the strain until it reaches zero after some time. Show that the stress
drops exponentially with time, and the strain approaches a constant exponentially.
3 Mechanical Aspects of Biosystems
Determine the stress on the discs when the woman stands. During the day, after
4 h, the strain of the cervical region has become 2%, which is 60% of its longperiod strain. The spine expands back to its original length during the night when the
body is prone. There is little compression of the vertebrae between the intervertebral
discs.
Fit this data to a Kelvin-Voigt model of the intervertebral discs.
Plot the predicted strain as a function of time (in hours) during the day.
3.14 A 45 kg woman jumps from a height of 2.5 m to a solid floor. In an attempt
to minimize the likelihood of injury, she lands on the ball of her feet (the pads just
behind her toes) with her knees bent. What average force is needed on her feet to
stop her fall if her center-of-gravity after touching the floor drops 80 cm before she
stops? If the horizontal distance from the ball of her foot to her talus (where her tibia
exerts its force) is 15 cm, and from talus back to the Achilles tendon is 3.6 cm, what
average force does the Achilles tendon suffer during the stopping time?
3.15 The bone around your teeth behaves somewhat like a Maxwell viscoelastic
material. When stressed by the pressure of a tooth, the bone, over time, moves to
relieve the stress. Suppose we find that the stress on the bone next to a tooth drops
linearly with the strain until it reaches zero after some time. Show that the stress
drops exponentially with time, and the strain approaches a constant exponentially.