Problems
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engines? If the flagellum motor is powered by 7.8 × 10 4 protons per second passing
through a potential difference of 140 mV, causing the flagellum to rotate at 70 times
per second, what torque does the motor develop?
3.4 If a spacecraft in the shape of a doughnut, of radius 400 m, is spun around
its natural axis, what angular speed is needed to make humans feel natural gravity
standing on the inner shell of the doughnut?
3.5 Apply Stokes’ Law in the form F v = b v to a person of mass 50 kg standing
against the 44 m/s wind of a Hurricane. If the center-of-mass of that person is 1.2 m
high and 0.4 m shifted horizontally from the pivot point at the feet, what is the air
drag coefficient b for that person? (Assume that the effect of the wind on the person
is the same as a force F v on the center-of-mass.)
3.6 Determine the sedimentation speed for a hemoglobin molecule in a centrifuge
with the molecule at a radius of 20 cm from the axis and a rotational acceleration of
100,000 g. Take the hemoglobin molecule as having a mass of 8000 Da and a radius
of 0.0027 microns, and the plasma having a density 1.025 g per cubic centimeters
and a viscosity of 0.015 poise.
3.7 The wind on Mars can reach 27 m/s (60 mph). The temperature of that wind in
the midday Sun is about 20 ◦ C (70 ◦ F) but the atmosphere is only 1% as dense as at
the surface of the Earth at the same temperature. For simplicity, suppose that a man’s
effective surface area of 0.5 m 2 stops all the momentum of the wind hitting it. Show
that the force depends on the square of the speed of the wind (unlike the Stokes’
drag force). Estimate the force of that Martian wind on a man standing against it.
3.8 An air bubble of diameter 0.45 mm is observed at a depth of 3.6 cm in blood
plasma. Estimate the pressure in that bubble.
3.9 For a sitting person with a cuff pressure of 120/80 mmHg, what would you
predict for the pressure in the carotid artery?
3.10 Amusement parks have rides which produce up to ‘4g’ on the riders. If a 2 m
high person’s body is along the direction of the acceleration of the ride, what would
be the difference in blood pressure from his head to toe?
3.11 If the compliance C of an aorta is measured to be 2.67 × 10 −4 ml/mmHg,
what change occurs in its volume as the heart creates a systolic gauge pressure of
120 mmHg compared to a diastolic gauge pressure of 70 mmHg. Estimate the extra
elastic energy stored in the walls of the aorta at systole?
3.12 If a certain astronaut’s lung has a compliance of 140 ml/mmHg, how much
larger might his lung expand elastically if, during a space walk, his spacesuit loses
pressure while he holds his breath?
3.13 Suppose the cervical region of the spine of a woman holds up her head,
of mass 4.5 kg. The intervertebral discs make up about 25% of a length 11.5 cm
for the cervical region, containing six such discs of cross-sectional area 145 mm 2 .
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engines? If the flagellum motor is powered by 7.8 × 10 4 protons per second passing
through a potential difference of 140 mV, causing the flagellum to rotate at 70 times
per second, what torque does the motor develop?
3.4 If a spacecraft in the shape of a doughnut, of radius 400 m, is spun around
its natural axis, what angular speed is needed to make humans feel natural gravity
standing on the inner shell of the doughnut?
3.5 Apply Stokes’ Law in the form F v = b v to a person of mass 50 kg standing
against the 44 m/s wind of a Hurricane. If the center-of-mass of that person is 1.2 m
high and 0.4 m shifted horizontally from the pivot point at the feet, what is the air
drag coefficient b for that person? (Assume that the effect of the wind on the person
is the same as a force F v on the center-of-mass.)
3.6 Determine the sedimentation speed for a hemoglobin molecule in a centrifuge
with the molecule at a radius of 20 cm from the axis and a rotational acceleration of
100,000 g. Take the hemoglobin molecule as having a mass of 8000 Da and a radius
of 0.0027 microns, and the plasma having a density 1.025 g per cubic centimeters
and a viscosity of 0.015 poise.
3.7 The wind on Mars can reach 27 m/s (60 mph). The temperature of that wind in
the midday Sun is about 20 ◦ C (70 ◦ F) but the atmosphere is only 1% as dense as at
the surface of the Earth at the same temperature. For simplicity, suppose that a man’s
effective surface area of 0.5 m 2 stops all the momentum of the wind hitting it. Show
that the force depends on the square of the speed of the wind (unlike the Stokes’
drag force). Estimate the force of that Martian wind on a man standing against it.
3.8 An air bubble of diameter 0.45 mm is observed at a depth of 3.6 cm in blood
plasma. Estimate the pressure in that bubble.
3.9 For a sitting person with a cuff pressure of 120/80 mmHg, what would you
predict for the pressure in the carotid artery?
3.10 Amusement parks have rides which produce up to ‘4g’ on the riders. If a 2 m
high person’s body is along the direction of the acceleration of the ride, what would
be the difference in blood pressure from his head to toe?
3.11 If the compliance C of an aorta is measured to be 2.67 × 10 −4 ml/mmHg,
what change occurs in its volume as the heart creates a systolic gauge pressure of
120 mmHg compared to a diastolic gauge pressure of 70 mmHg. Estimate the extra
elastic energy stored in the walls of the aorta at systole?
3.12 If a certain astronaut’s lung has a compliance of 140 ml/mmHg, how much
larger might his lung expand elastically if, during a space walk, his spacesuit loses
pressure while he holds his breath?
3.13 Suppose the cervical region of the spine of a woman holds up her head,
of mass 4.5 kg. The intervertebral discs make up about 25% of a length 11.5 cm
for the cervical region, containing six such discs of cross-sectional area 145 mm 2 .