Kinesiology 201 Questions
Kinetics
Tony Leyland
School of Kinesiology
Simon Fraser University
1.
A javelin thrower exerts an impulse of 25 Ns on a 800 gram javelin. Assume that at the
start of the final step and throw phase the velocity of the javelin is 2 ms-1 and the centre
of gravity of the javelin is 1 m above the ground. The height of the centre of gravity of
the javelin at release is 1.6 m and the distance the javelin travels between these two
points is 4 m.
a) What is the release speed of the javelin? [3]
b) What is the mechanical energy of the javelin at release? [3]
c) What is the average force he applies to the javelin? [3]
2. You are evaluating a workplace where there have been some complaints about a task
requiring a loaded cart be pushed up a ramp. The wheeled cart has a mass 120 kg, the
ramp is at an angle of 15o, and the coefficient of friction between the wheels and the ramp
is constant at 0.01
a) What is the minimum force a worker must apply parallel to the ramp’s surface to
move the cart up the ramp? [3]
b) The average mass of the workforce is 70 kg and the average coefficient of friction
between their shoes and the ramp is 0.45. Using these values determine whether it
is likely they will slip. [5]
c) What could they do to reduce their chances of slipping? [2]
3. The vertical ground reaction
force of a 61.16 kg (600 N)
subject
while
running
is
approximated opposite.
The
thick dashed line represents
body weight.
1400
1000
Force
(N)
Body
Weight
a) How long is she in contact with
the ground? [1]
b) What is the net impulse she
experiences during the contact
phase with the ground? [6]
0 25 50 100
200
230 250
c) If she leaves the ground with the
Time (milliseconds)
same centre of gravity vertical
speed as she lands with, what must that speed be? [4]
d) How would you use this information to determine where during the support phase of
running her vertical velocity is equal to zero? No calculation is required for this part of the
question. [2]
1
4. Define the following laws.
a) Conservation of mechanical energy. [2]
b) Rotational analogue of Newton's 1st law of motion. [2]
c) Rotational analogue of Newton’s 2nd law of motion. [2]
5.
6.
What is the most common form of lever in the human musculoskeletal system? List one
advantage of this type of lever. [2]
What variable am I calculating if I calculate the area under a:
a) force-time curve? [1]
b) force-displacement curve? [1]
c) moment (torque)-angular displacement curve? [1]
7. Give the S.I. units and the fundamental units (MLT notation) of
a) power [2]
b) Energy [2]
c) moment of force [2]
8. Explain, using mechanical principles, why the subject would begin
turning if he pushed the spinning wheel into his chest. A diagram of
this manoeuvre is shown opposite. [5]
9.
Explain using mechanical principles, why a
person standing on a frictionless turntable
would begin turning when he turned the
spinning wheel from a vertical plane to a
horizontal plane. Be sure to indicate which
direction(s) the wheel and the subject are
spinning. A diagram of this manoeuvre is
shown opposite. [5]
10. A Muscle Moment-Time graph is shown
opposite for the muscle moment generated by
the quadriceps during a knee extension
exercise (assume the thigh remains stationary).
a) If the moment of inertia of the shank & foot is
0.7 kg.m2, what would the angular velocity of
the knee be at time = 0.2 seconds? Assume
the knee starts from a static flexed position. [3]
b) What is the peak angular acceleration at the
knee during these 0.2 seconds? [2]
c) What is the muscle moment power output of the
quadriceps at time = 0.1 seconds? [3]
150
Moment
(Nm)
0
0.1
0.2
Time (seconds)
2
11. A person throws a discus (mass = 2 kg) at an angle of 40o to the horizontal with a velocity
of 20 m/s. Neglect air resistance for these questions.
a) What is the mechanical energy of the discus at release (relative to the ground) and just
prior to contact with the ground (assume no rotational energy)? [4]
b) Calculate the distance the object travelled horizontally prior to ground contact if the
discus was released 1.5 m above the ground. [6]
c) Are these reasonable calculations to make (i.e. are the answers to part a and b going to
be somewhat accurate)? [5]
12. a) The table opposite gives the displacementtime data for a 100 m sprint race. If the mass
of the athlete is 70 kg what is the net impulse
generated over the first five seconds of the
race? Assume the athlete starts at time 0.0
seconds with zero velocity. [4]
b) What is the net impulse generated over the
next five seconds (5-10 seconds)? [4]
c) What is the average force generated over
these first 5 seconds? How does this compare
to the peak force over these 5 seconds? What
is the best estimate of peak force you can
calculate (hint: it can be calculated using data
in this table and the mass of the athlete). [5]
d) Is the peak force calculated in part c) likely to
be close to the true peak force? Explain. [2]
Time (s)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
Displ. (m)
0.000
0.857
3.160
6.484
10.564
15.210
20.266
25.603
31.130
36.774
42.480
48.213
53.951
59.688
65.422
71.160
76.897
82.635
88.373
94.111
99.844
105.514
13. The diagram opposite shows a model of the femur
(segment 1) and tibia (segment 2)
a) If the joint force (Fj) equals 500 N, and the
velocity of the joint (Vj) equals 5 m/s and θ
equals 30o, what is the Joint Force Power at
this joint? [2]
b) In which direction is energy being transferred
across this joint? [2]
c) If this situation continues for 0.6 seconds how
much work is done on the femur? [2]
Fj
θ
Vj
Vj
-Fj
3
Force
14. Opposite is an antero-posterior
(horizontal) ground reaction force
vs. time graph for level ground
walking. Draw an approximate
velocity-time
graph
for
the
individual’s centre of gravity
(remember F= ma). [5]
Time
15. You are moving a heavy desk.
Explain the mechanical advantages
and disadvantages of ether pulling
or pushing the desk. Do not just
focus on the biomechanics of the
human, be sure to discuss friction
in your answer. [5]
Total angular momentum
16. What activity could the graph
opposite be associated with? Briefly
explain the reasons for the change
in these two variables. [5]
Moment
of inertia
Angular
velocity
Time
17. a) What muscles are active in the down phase of an overhead press? [3]
b) Explain how you can deduce your answer for part a above from a work-energy
perspective. [2]
The barbell system weighs 60 kg. The weight lifter lowers the barbell (from rest) 0.35 m, at
which point it is moving at 0.5 m/s.
c) What is the amount of external work he has done on the barbell to this point? [9]
d) Is he performing negative or positive work on the barbell? [2]
e) Is the total work done on the barbell (answers from parts c) likely to be close to the total
metabolic energy output for this activity? Explain. [4]
18. Explain what is happening if someone was working in the “negative power” portion of the
power-velocity curve. [5]
4
19. A company calls you in because of a reasonably high number of accidents at their plant
that are due to slips. Briefly list what factors would you consider in your analysis? [5]
20. This data is the same as question 11 with a different slant to the question. A person
throws a discus (mass = 2 kg) at an angle of 40o to the horizontal with a velocity of 20
m/s. Deduce the horizontal and vertical impulses he must have applied to achieve the
release velocity if the implement started from rest and he applied this impulse for 2
seconds. [7]
(59.7, 78.7)
21. Calculate the co-ordinate position of
the centre of gravity of the entire leg
segment shown below. The leg is
modelled as only two segments for
simplicity. The anthropometry is given
in the table below (radius of gyration is
included as it is needed in question 22
not now). The co-ordinate data (in cm)
of the ankle, knee and hip joint centres
are shown on the diagram.
The
location of the C of g of the combined
shank and foot segment is given
relative to the shank length.
The
shank is aligned vertically and the thigh
is at a 45o angle. [10]
Segment
Thigh
Shank &
Foot
Mass
(kg)
7 kg
4 kg
Length
(cm)
42 cm
44 cm
(shank)
% distance to C of g
from proximal joint
44% of thigh length
60% of shank length
45o
(30, 49)
(30, 5)
Radius of gyration (k)
from proximal joint
0.22
0.32
22. The same as above subject performs a seated knee extension during a rehab session.
He extends from a static flexed 90o position towards a fully extended position. His thigh
does not move during this exercise. In addition to the mass, length and c of g location
above the radius of gyration of the two segments
a) His initial peak shank & foot segment acceleration is 100 radians per second2, calculate
the peak torque generated by his quadriceps. [4]
b) As he passes through 45o of flexion his angular velocity is 10 radians/second. This
movement takes 0.21 seconds. What was his net impulse and average net musclemoment output during this time? [7]
c) Is the value you calculated for part b) likely to close to the real muscle moment? Discuss
the many factors that you would have to take into account to get an accurate measure of
the true quadriceps muscle moment (no calculation needed). [4]
5
23. Kinematic data for a subject walking is listed on page 3 of the kinematics section. All coordinate data is this table is in millimetres for the right leg. Below is the relevant
anthropometry for the subject.
Segment
Thigh
Shank
Foot
Mass
(kg)
7
3
1
Length
(cm)
40.5
39.6
27.7
% distance to C of g
from proximal joint
44%
44%
50%
radius of gyration (k)
from proximal joint
0.22
0.21
0.19
a) Calculate the shank angular velocity at frame 7? [10]
b) What is the potential energy of the shank at frame 7 (hint the y values are the distance off
the ground)? [5]
c) What is the rotational kinetic energy of the shank at frame 7? [3]
d) Briefly explain how would you calculate the translational kinetic energy of the shank at
frame 7 (no calculation required)? Obviously linear kinetic energy = ½mv2 but how would
you calculate the velocity of the shank’s C of g? [4]
24. a) Calculate the torque-impulse that must
have been produced by a combination
of gravitational torque (as mg acts
some distance from axis of rotation)
and triceps moment given the
information opposite.
b) If this movement took 0.1 seconds, what
would the average torque have been?
c) Ignoring the effect of gravity calculate the
work done by the triceps?
θi = 0 rads/s
θi = -20 rads/s
t =0.1s
Forearm/hand segment moment
of inertia about elbow, Ie = 0.25 kgm2
25. The diver opposite leaves the board with a take-off velocity
of 5 m/s at an angle of 120o to the right horizontal. The
forward angular momentum of the diver at take-off is 35
kg.m2/s and the tightest tuck position she can obtain gives
her a moment of inertia of 3 kg m2. Her centre of gravity
falls 5 m vertically from the time she leaves the board to
when she enters the water.
How many forward
somersaults (complete revolutions) can she perform if she
enters the water head first? Show all working out (just
writing the answer is a maximum of 2 marks). [10]
26. A weight lifter raises a barbell and weights (mass 75 kg) 0.8m vertically. Later
using a friend to help raise the barbell, he performs a negative set where he
lowers a mass of 100 kg. He is not able to press this amount of mass upwards.
a) How much work is performed during the concentric phase of this movement?
b) What more information would you need to know to be able to determine his power
output? [1]
c) Why is he able to lower a greater mass than he can lift? [2]
6
27. a)
List all errors in the following statement. "When inflated to regulation pressure, the
coefficient of restitution of a basketball is 1.16m". [3]
b) A volleyball is dropped from a height of 2m onto a hardwood floor. It rebounds to a
height of 1.1 m, what is the coefficient of restitution between the ball and floor? [3]
c) List what factors would affect the COR of a squash ball hitting the court wall? [3]
28. Define or explain the following terms: [2 marks each]
a) Newton's first law of motion
b) Work (what units is this measured in?)
c) Power (explain with reference to human muscular contraction)
d) Centripetal Force.
e) Free Body Diagram
f) Resistive Force
g) Coefficient of limiting friction (what units is it measured in?)
h) Pressure (what units is it measured in?)
29. Using two of the equations given on the equations page in your answer, describe the
mechanical justification for protective equipment in sports. An example might be shin
pads and padded goalkeepers jerseys in soccer, shoulder, elbow, and knee pads in
hockey. Hint: think of my “catching a cricket ball” example (that should get you on
the track for one of those equations). If I haven't demonstrated that yet, then come
and ask me. [5]
30.
State the law of conservation of angular momentum. Athletes can initiate rotation (e.g.
cat rotation) and offset angular rotation (e.g. long jump) whilst in the air in apparent
contradiction of this law. Explain in detail, using equations wherever possible, how all
the movements they perform in both these skills achieve the desired outcomes. [12]
31. Calculate the location of the centre of gravity of the system below from the left edge of
the black beam. The distances given are the displacements of the three box's centre of
gravity from this point. Ignore the weight of this beam. [10]
100 N
80 N
15 N
10 cm
50 cm
1m
32. How much work is required in the horizontal direction to catch a 1.3kg ball travelling at a
horizontal velocity of 30 m/s (assuming you reduce the balls horizontal velocity to zero)?
If you take 0.5 seconds to perform this catch, what is the average force you must apply
on the ball? [6]
33. A single equivalent muscle representing the forearm flexors (shown overleaf) is capable
of producing 1500 N and its tendon attaches 0.03 m from the joint axis of rotation.
Assume the line of action of the muscle is parallel to the humerus.
7
a) What torque would this muscle
produce at a relative joint angle of
150o? [4]
1500 N
b) If the limb segment this muscle
moves has a mass of 3kg with a
radius of gyration of 0.3m, what
angular acceleration would this
torque produce? Ignore the effect
of gravity for this calculation. [6]
150o
60o
0.03 m
34. For this question use the co-ordinate date given on page 19.
a) Calculate the thigh's total energy at frame 3, given the following anthropometry. This
individual is not the 50% male from the tables. [10]
1. Mass of the thigh = 7 kg
2. Location of C of G of thigh = 43% of segment length from proximal joint.
3. Radius of gyration/segment length = 0.323
35. Calculate the instantaneous translational (ag) and rotational acceleration (α) vectors of
the whole body in the jump represented by the diagram below. F is the ground reaction
force; r is the distance of a line from the application point of F to the body's centre of
gravity; θ is the angle of this line; φ is the angle of the vector F; Ιg is the body's moment of
inertia about a transverse axis passing through the centre of gravity; and m is the mass of
the subject. What activity do you think he would likely be performing? Briefly justify your
answer. Do not forget about gravity! [10]
F
F = 1000 N
r = 1.2 m
θ = 1.2 rad
φ = 1.7 rad
Ιg = 12 kgm2
m = 70 kg
r
φ
θ
36. A cyclist (mass of cyclist and bike = 80 kg) negotiates a velodrome curve at a tangential
velocity of 20 m/s. If the radius of the curve is 35 m and the track is banked at 20o what
is the component of centrifugal force exerted up the slope by the tires? Explain whether
or not all of this force is opposed by friction? Also calculate the normal force he exerts
against the track. Is this normal force, greater or less than mg, explain? [5]
8