ProblemSet4_Fa23
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School
University of Massachusetts, Amherst *
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Course
430
Subject
Health Science
Date
Dec 6, 2023
Type
Pages
5
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NAME___________________________________
KIN 430 – Biomechanics
Fall Semester 2023
Problem Set #4 (25 points) – Due on by 5:00pm Wednesday Dec 6th, 2023
Answer the following questions by placing your answers in the spaces provided. Do all of your calculations on
separate sheets of paper, clearly indicating which calculations go with which problems.
You must show your
calculations to receive full credit, even if you have the correct answers
. Don’t forget to include proper units!
1.
(2 pts.)
Lionel Messi who weighs 805 N jumps up in the air to perform a “bicycle kick” (see figure). If
the moment of inertia of his whole body relative to an axis through his center of mass is 7.2 kg*m
2
, what
is his radius of gyration in this posture?
https://www.youtube.com/watch?v=i9lKiGm6UtM
Radius of Gyration ______________
2.
(3 pts.)
A kinesiology student competed in the Du Bois Library Tower Run while measuring his oxygen
consumption by wearing a portable respirometer. The student had a mass of 73 kg and the Du Bois library
has 440 steps with a vertical rise of 17.9 cm per step. It took him 140 s to complete the tower run. Based
on this information, determine how much mechanical work the student did. From his oxygen consumption
it was estimated that he expended metabolic energy at a rate of 22.3 kcal/min while running up the stairs.
Based on this information, determine his percent movement efficiency (Hint: 1 J = 0.000239 Kcals).
Mechanical work: _____________
Efficiency (%): _____________
NAME___________________________________
3. (4 pts.)
A UMass diver is training for the Atlantic10 championship and wants to know how his angular
momentum will impact the number of aerial summersaults he can perform from a 5.2 m platform dive.
He initially
leaves the platform with a 2.5 m/s vertical velocity and 95.5 kg·m
2
/s of angular momentum. Neglect any height
differences that may arise from having the center of mass above the diving board and from incomplete turns at
water impact.
A) How long will it take him to hit the water?
B) How many summersaults will he complete if his moment of inertia is 9 kg·m
2
?
C) How many summersaults will he complete if it is 2 kg·m
2
?
D) And what should his average moment of inertia be if he aims to perform exactly 2.5 summersaults?
Total time in the air: _________
Summersaults at 9 kg·m
2
: ______________
Summersaults at 2 kg·m
2
: ______________
Moment of Inertia for 2.5 summersaults: ______________
4. (4 pts.)
As a person is running, their soleus, gastrocnemius and tibialis anterior muscles generate forces about
their ankle joint. During late stance, the magnitudes of the forces are soleus 1550 N and tibialis anterior 825 N.
The magnitudes of the muscle moment arms about the ankle joint are soleus 0.06 m, gastrocnemius 0.07 m, and
tibialis anterior 0.04 m. What is the force generated by the gastrocnemius muscle if the net torque is -150 N m
(negative = plantarflexion)? What is the force generated by the gastrocnemius if the net torque is -75 N m
(negative = plantarflexion)?
Gastrocnemius muscle force at net torque of -150 N m ____________
Gastrocnemius muscle force at net torque of -75 N m ____________
NAME___________________________________
5
. (6pts) A person holds a box with a mass of 25 kg in two positions relative to the sacroiliac joint (S1in image
below). In the position with the arms more extended, the center of mass of the box is 55 cm (0.55 m) from the S1
joint, while in the position with the arms more flexed, the center of mass of the box is 30 cm (0.30 m) from the
S1 joint. If the back extensor muscles operate with a moment arm of 4.7 cm (0.047 m) relative to the S1 joint,
how much force do the back extensor muscles need to generate while holding the box statically in these two
positions
?
If we assume the individual weights 81 kgs and the combined center of mass of the head, arms and
trunk are directly over the S1 and make up 68% of that person’s total weight, how much force is there on the S1
joint in both positions.
Draw the FBD (use a generic ‘r
box
’ for the box so that you only need to draw 1 FBD that
represents both scenarios).
Torque produced by the box about the S1 joint
Extended arm position:
__________________
Flexed arm position:
__________________
Back extensor muscle force
Extended arm position:
__________________
Flexed arm position:
__________________
S1 Joint Force
Extended arm position:
__________________
Flexed arm position:
__________________
DRAW
FBD:
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NAME___________________________________
6. (3 pts.)
A figure skater who weighs 560 N is spinning about her longitudinal axis during a jump at a rate of
3.14 rad/s (or half a revolution per second) in position A. If her radius of gyration in position A is 0.19 m what is
her angular momentum? If she pulls her arms in toward her chest, decreasing her radius of gyration to 0.11 m in
position B, what will her angular momentum and her angular velocity be (in radians per second and revolutions
per second, Hint: 2
࠵?
radians equals 1 revolution)?
Angular Momentum in A ______________
Position A
Position B
Angular Momentum in B ______________
Angular Velocity in B in radians per second ______________
Angular Velocity in B in revolutions per second ______________
NAME___________________________________
5. (3 pts.)
Your personal training client is doing leg curls on a Cybex machine when she pauses at a 90
°
knee joint
angle (see figure below). The force exerted by the machine (F
C
) on her leg is 520 N, directed at an angle of 60
°
relative to the tibia (angle
a
) and the distance from her knee joint to the point where the force is applied is 0.43
m (distance L). For this problem, assume the weight of the shank and foot is negligible and that the muscle force
(F
M
) acts perpendicular to the tibia in this position with a moment arm of 0.08 m (distance d) relative to the knee.
How much torque is the machine producing, and how much force do the muscles (F
M
) need to generate to hold
this position?
Torque about knee produced by machine:
___________
Hamstring Muscle Force:
_____________
d = 0.08 m
F
L = 0.43
F
C
hip
knee
fo
a