Calculate the strain and change of length of the femur during a single step while running. (Use t described in the discussion near equation 4.21) Energy Storage in Tendons and Long Bones Let us return to the example of running in Fig. 3.34 [2]. The force on the Achilles tendon is 4,700N. With a cross-sectional area of 89 mm², we see that 4,500 N/89 mm² = 53 N/mm² = 53 MPa. Given the maximum stress for tendons, the UTS, is ~100 N/mm² = 100MPa, during running the stress in these tendons is not far from the damage threshold. It is not surprising that the Achilles tendons of athletes occasionally snap, either partially or totally. Using the stress-strain relation shown in Fig.4.14, this stress leads to a strain of 0.06 6%. The length of the Achilles tendon is Lo= 250mm, so this strain corresponds to the tendon lengthening by 15 mm and -TJE Va+AL=(53 N/mm = 35,000 N-mm = 35 N-m = 35 J. PE= Clamp This is exactly the amount of energy we stated was being stored in the Achilles tendon during every step of a run. How much energy is stored in the bones during this step? Let us examine the largest bone, the femur. We will use Lo 0.5 m and so V 165,000 mm³. Also Y = 500 mm and A = 330 mm². - 17, 900 MPa = 17,900 N/mm². The upward Tendon Load cell to -Extensometer Tit (53 -Actuator N/mm²)(0.06) (89 mm²) (250 mm) (4.18) (4.19) Stress (newtons per square millimetre) 60- 40- 0 = Strain (%) Fig. 4.14 Stress-strain (or force-length) for a human big toe flexor tendon, using the instrument on the left, with a 2-s-long stretch and recoil cycle. (From [2]. Copyright 1992 Columbia University Press. Reprinted with the permission of the Press)
Calculate the strain and change of length of the femur during a single step while running. (Use t described in the discussion near equation 4.21) Energy Storage in Tendons and Long Bones Let us return to the example of running in Fig. 3.34 [2]. The force on the Achilles tendon is 4,700N. With a cross-sectional area of 89 mm², we see that 4,500 N/89 mm² = 53 N/mm² = 53 MPa. Given the maximum stress for tendons, the UTS, is ~100 N/mm² = 100MPa, during running the stress in these tendons is not far from the damage threshold. It is not surprising that the Achilles tendons of athletes occasionally snap, either partially or totally. Using the stress-strain relation shown in Fig.4.14, this stress leads to a strain of 0.06 6%. The length of the Achilles tendon is Lo= 250mm, so this strain corresponds to the tendon lengthening by 15 mm and -TJE Va+AL=(53 N/mm = 35,000 N-mm = 35 N-m = 35 J. PE= Clamp This is exactly the amount of energy we stated was being stored in the Achilles tendon during every step of a run. How much energy is stored in the bones during this step? Let us examine the largest bone, the femur. We will use Lo 0.5 m and so V 165,000 mm³. Also Y = 500 mm and A = 330 mm². - 17, 900 MPa = 17,900 N/mm². The upward Tendon Load cell to -Extensometer Tit (53 -Actuator N/mm²)(0.06) (89 mm²) (250 mm) (4.18) (4.19) Stress (newtons per square millimetre) 60- 40- 0 = Strain (%) Fig. 4.14 Stress-strain (or force-length) for a human big toe flexor tendon, using the instrument on the left, with a 2-s-long stretch and recoil cycle. (From [2]. Copyright 1992 Columbia University Press. Reprinted with the permission of the Press)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
Femur
![Calculate the strain and change of length of the femur during a single step while running. (Use the data
described in the discussion near equation 4.21)
Energy Storage in Tendons and Long Bones
Let us return to the example of running in Fig. 3.34 [2]. The force on the
Achilles tendon is 4,700N. With a cross-sectional arca of 89 mm?, we see that
4, 500N/89 mm?
tendons, the UTS, is -100 N/mm2 = 100MPA, during running the stress in these
tendons is not far from the damage threshold. It is not surprising that the Achilles
tendons of athletes occasionally snap, either partially or totally.
Using the stress-strain relation shown in Fig.4.14, this stress leads to a strain
of 0.06
53 N/mm? = 53 MPa. Given the maximum stress for
250mm, so this strain
6%. The length of the Achilles tendon is Lo
corresponds to the tendon lengthening by 15 mm and
oev =
reAla = (53 N/mm?)(0.06)(89 mm²)(250 mm) (4.18)
PE =
geV
= 35, 000 N-mm = 35 N-m = 35J.
(4.19)
%3D
This is exactly the amount of energy we stated was being stored in the Achilles
tendon during every step of a run.
How much energy is stored in the bones during this step? Let us examine the
largest bone, the femur. We will use Lo
I so
500 mm and A = 330 mm2.
17,900 N/mm?. The upward
0.5 m
and so V =
165, 000 mm. Also Y = 17, 900 MPa
60-
Load cell
Clamp-
to
40-
Tendon
Extensometer
-Actuator
Strain (%)
Fig. 4.14 Stress -strain (or force length) for a human big toe flexor tendon, using the instrument
on the lefi, with a 2-s-lang stretch and recoil cycle. (From [2]. Copyright 1992 Columbia University
Press. Reprinted with the permissiun of the Press)
Stress (newtons per square millimetre)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49802ebc-5fcb-404d-a8e9-d9e7cc54a186%2F0fb2b68f-8427-4850-be7e-b120ff71139a%2Fulgs2la_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Calculate the strain and change of length of the femur during a single step while running. (Use the data
described in the discussion near equation 4.21)
Energy Storage in Tendons and Long Bones
Let us return to the example of running in Fig. 3.34 [2]. The force on the
Achilles tendon is 4,700N. With a cross-sectional arca of 89 mm?, we see that
4, 500N/89 mm?
tendons, the UTS, is -100 N/mm2 = 100MPA, during running the stress in these
tendons is not far from the damage threshold. It is not surprising that the Achilles
tendons of athletes occasionally snap, either partially or totally.
Using the stress-strain relation shown in Fig.4.14, this stress leads to a strain
of 0.06
53 N/mm? = 53 MPa. Given the maximum stress for
250mm, so this strain
6%. The length of the Achilles tendon is Lo
corresponds to the tendon lengthening by 15 mm and
oev =
reAla = (53 N/mm?)(0.06)(89 mm²)(250 mm) (4.18)
PE =
geV
= 35, 000 N-mm = 35 N-m = 35J.
(4.19)
%3D
This is exactly the amount of energy we stated was being stored in the Achilles
tendon during every step of a run.
How much energy is stored in the bones during this step? Let us examine the
largest bone, the femur. We will use Lo
I so
500 mm and A = 330 mm2.
17,900 N/mm?. The upward
0.5 m
and so V =
165, 000 mm. Also Y = 17, 900 MPa
60-
Load cell
Clamp-
to
40-
Tendon
Extensometer
-Actuator
Strain (%)
Fig. 4.14 Stress -strain (or force length) for a human big toe flexor tendon, using the instrument
on the lefi, with a 2-s-lang stretch and recoil cycle. (From [2]. Copyright 1992 Columbia University
Press. Reprinted with the permissiun of the Press)
Stress (newtons per square millimetre)
![normal force in Fig. 3.34 is 6,400N, which we will assume is transmitted all the way
to the femur. The stress is 6, 400 N/330 mm? = 19,4 N/mm' and
1 (19.4 N/mm)?
2 17,900 N/mm?
= 1,730 N-mm = 1.73 N-m ~ 2J.
PE =
2 Y
165,000 mm3
(4.20)
(4.21)
If the same enegry is stored in the tibia and fibula, then at most ~3-4J is stored in
these long bones, which is a very small fraction of the 10OJ kinetic energy lost per
step.
Elastic energy recovery from tendons and ligaments may be important in motion,
which means the energy storage is mostly elastic, it can be recovered in phase (which
often means fast enough) to assist the motion, and failures due to stresses at high
loading values and repetitive actions are not attained [66]. Longer tendons, such as
Achilles tendons in the lower limb (120mm long), can stretch more and tend to
store more energy than shorter tendons (why?), but recoil and release the energy
slower. These shorter tendons include the shoulder internal rotator muscle tendons
used in throwing (-58 mm) and the patellar tendon (48 mm). While the shorter
tendons in the shoulder store less energy per tendon, there are many in parallel so
much energy can still be stored in them and in shoulder ligaments, and with faster
release.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49802ebc-5fcb-404d-a8e9-d9e7cc54a186%2F0fb2b68f-8427-4850-be7e-b120ff71139a%2Fxe42jl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:normal force in Fig. 3.34 is 6,400N, which we will assume is transmitted all the way
to the femur. The stress is 6, 400 N/330 mm? = 19,4 N/mm' and
1 (19.4 N/mm)?
2 17,900 N/mm?
= 1,730 N-mm = 1.73 N-m ~ 2J.
PE =
2 Y
165,000 mm3
(4.20)
(4.21)
If the same enegry is stored in the tibia and fibula, then at most ~3-4J is stored in
these long bones, which is a very small fraction of the 10OJ kinetic energy lost per
step.
Elastic energy recovery from tendons and ligaments may be important in motion,
which means the energy storage is mostly elastic, it can be recovered in phase (which
often means fast enough) to assist the motion, and failures due to stresses at high
loading values and repetitive actions are not attained [66]. Longer tendons, such as
Achilles tendons in the lower limb (120mm long), can stretch more and tend to
store more energy than shorter tendons (why?), but recoil and release the energy
slower. These shorter tendons include the shoulder internal rotator muscle tendons
used in throwing (-58 mm) and the patellar tendon (48 mm). While the shorter
tendons in the shoulder store less energy per tendon, there are many in parallel so
much energy can still be stored in them and in shoulder ligaments, and with faster
release.
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