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Unformatted text preview: ME
577
–
Human
Motion
Kinetics
Exam
1
Wherever
possible
use
our
four
step
method.
1. Particle
problem:
A
diver
with
a
mass
of
70
kg
drops
from
a
10
meter
platform
with
an
initial
vertical
velocity
of
0
m/s.
What
is
the
diver’s
vertical
speed
when
he
or
she
impacts
the
water?
How
long
does
it
take
for
the
diver
to
hit
the
water?
Tomb
of
the
Diver,
Paestum,
Italy
(a
Greek
fresco
dated
to
470
BC).
2.
Particle:
Assume
a
fastball
crosses
the
plate
traveling
horizontally
at
a
speed
of
22.1
m/s.
To
stop
the
ball,
the
catcher’s
mitt
(and
the
catcher’s
arm)
gives
a
little
bit.
The
ball
is
stopped
over
a
distance
of
0.15
m.
Assume
the
catcher’s
mitt
exerts
a
constant
force
on
the
ball.
What
is
that
force?
Twins
catcher,
Joe
Mauer
3.
Particle:
Two
ice
skaters
start
out
motionless
in
the
center
of
an
ice
rink.
They
then
push
each
other
apart.
The
male
partner
has
a
mass
of
80
kg
and
moves
to
the
left
at
a
speed
of
1.5
m/s.
If
the
female
partner
has
a
mass
of
58
kg,
how
fast
does
she
move?
Which
direction
does
she
move?
What
is
the
change
in
momentum
of
the
two
skaters?
What
is
the
change
in
energy
of
the
two
skaters?
4.
Rigid
Body
(Pay
attention
to
what
is
asked
–
we
are
not
solving
the
entire
problem):
A
weight
lifter
starts
with
his
hands
at
his
sides
and
raises
his
arms
90o
in
T=1
second,
π⎛
⎛ πt ⎞ ⎞
θ (t ) = ⎜ 1 − cos ⎜ ⎟ ⎟
⎝ T ⎠⎠
4⎝
.
His
arm
is
80
cm
long
and
rotates
about
the
center
of
the
humeral
head.
The
deltoid
attaches
at
a
point
approximately
9
cm
from
the
center
of
the
humeral
head.
For
simplicity,
assume
that
it
always
makes
an
angle
of
10o
with
the
long
axis
of
the
humerus.
The
weight
lifter
raises
a
weight
with
a
mass
of
30
kg.
4a.
Draw
a
free
body
diagram.
4b.
Write
out
the
equations
of
motion
that
govern
the
system.
4c.
Calculate
the
acceleration
of
the
center
of
mass.
4d.
If
the
mass
of
the
arm
is
25
kg,
determine
the
system’s
moment
of
inertia
relative
to
the
center
of
the
humeral
head.
5.
Anatomy
How
many
bones
are
there
in
the
human
skeleton?
What
is
the
longest
bone
in
the
human
body?
How
many
metacarpals
are
there
in
the
human
body?
Name ________________________________
ME 577 Human Motion Kinetics
Anatomy Quiz
1. Label the bones of the lower extremities (L1L7). (7 points). How many cervical, thoracic, and
lumbar vertebrae are there? Indicate the approximate locations of the cervical, thoracic and
lumbar segments. (6 points) Name ________________________________
2. Please label the following structures (note that you may not use some of the indicator lines and
there may not be lines to the structures you need to identify). (10 points)
Lateral collateral ligament
Medial collateral ligament
Anterior cruciate ligament
Posterior cruciate ligament
Lateral condyle
Medial condyle
Meniscus
Femur
Tibia
Fibula Name ________________________________
3. On the torso section below, please label both erector spinae muscles, both latissimus dorsi
muscles, and both rectus abdominus muscles. (6 points) Name ________________________________
4. In the picture of the skull (a), label the maxilla, mandible, and zygomatic bones. In the picture
of the cranium (label the cortical and cancellous bone). (5 points). Name ________________________________
5. List three vital or nearly vital organs that are protected by the rib cage. (3 points) 6. How many phalanges are there in the human body? (4 points) 7. List as many muscles as possible. (10 points)
7a. Which muscle(s) are responsible for flexion of the forearm? 7b. Which muscle(s) are responsible for extension of the lower leg? 7c. If you start with your arms at your side and abduct your entire arm, which muscle(s) are
responsible? 7d. Which muscle(s) are responsible for flexion of the lower leg? Name ________________________________
8. How does the knee maintain stability? Rank the factors in order of importance. (6 points) 9. Distinguish between an abduction and an adduction movement. (3 points) 10. Explain in words why optimization methods are often needed for determining muscle forces.
(4 points) Name______________________________________________ ME 577 Particles Exam Please complete the following problems. For each one, you should follow the four step process. In some cases, one or more of the steps may be done for you. Please note when this is the case. 1. The kinetic energy, T, is given by, 1
T = mv i v . 2 Differentiate the equation for kinetic energy. This is the power dissipation. If the applied force on the particle is a constant 12N in the E1 direction and, at a given instant, its velocity is, v = 3E1 + 4E2 + E3 m / s , ( ) calculate the power dissipation. Name______________________________________________ 2. Two ice skaters are moving at 6 m/s in the E1 direction (he has a mass of 85 kg and is facing forward, and she has a mass of 56 kg and is facing backwards). They then push each other apart. After they separate, she has a speed of 8.4 m/s in the E1 direction. What is the speed and direction of the male skater? Name______________________________________________ 3. Dodge Ball Problem This problem begins with a quote from a dodge ball website: http://columbusoh.about.com/od/sportsamateur/a/dodgeball.htm, “Dodge ball is usually thought of as just hurling a ball at someone. But surprisingly there are some rules.” Keep in mind that a regulation dodge ball is 8.5 inches in diameter. You will find that the rules for children are specially designed to damage the psyches if not the actual child. Adult Rules • Two teams, each team gets ten players per round • Substitutions may be made between rounds only • Each team may set their own formations but there must be at least 3 players within •
•
•
•
•
• 10 yards of the dividing line Players must never cross the dividing line First team to completely eliminate the opposing team wins that round; first team to win 10 rounds wins the match To eliminate a player you must hit him with a ball or catch a ball he has thrown Once a player is hit he must sit on the sidelines for the remainder of the round If a teammate catches an opposing player's throw he may designate one teammate who is out to return to the game Players who hit someone in the head must sit out the current round and the following round, with no substitution Rules for Children •
•
•
•
•
•
• • Divide 16 to 30 children into two teams One team forms a circle; the other team stands inside the circle Players forming the circle throw the ball at the players inside the circle Players inside the circle should run around and "dodge" the ball, trying to not get hit Hitting someone in the head doesn't count Only players in the outside circle may throw and catch the ball Players who get hit join the outside circle to begin throwing the ball at players in the inside circle The last player in the inside circle is the winner Name______________________________________________ 3. Continued Notice that, in both sets of rules, hitting a player in the head does not count. The question here is whether or not it is safe to avoid being knocked out of the game by putting your face in the path of the ball? Assume the mass of the head is 8% of body weight, the modulus of the head is 1.8 GPa and the effective modulus of the ball is 100 MPa. The mass of a dodge ball is 0.5 kg. If the force required to break a bone in the face or skull is approximately 3,000 N, how fast would the ball have to be thrown in order to break a bone? Is this a reasonable speed? 2.5 # 1 !t
&
HIC = ( !t ) % " adt (
$ !t 0
' 1
1
1
=
+
*
m
m1 m2
1
1
1
=
+
*
R
R1 R2
1
1
1
=
+
*
E
E1 E2
4
k = R*1/ 2 E *
3
. 2/5
" 5 m *Vz2 %
!m = $
# 4k '
&
tc = !m
Vz 3
Pm = k! m/ 2 . Name______________________________________________ 4. Beginning with Newton’s 2nd Law, derive the conservation of linear momentum for the impact of two particles. Please state all assumptions clearly. ...
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 Fall '09

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