42/77(a)
Semester 1, 2004
Page 1 of 6 pages
THE UNIVERSITY OF SYDNEY
FACULTY OF EDUCATION
EDUH 1017 SPORTS MECHANICS
JUNE 2004
Time allowed: TWO Hours
MARKS FOR QUESTIONS ARE AS INDICATED
TOTAL: 70 MARKS
INSTRUCTIONS
•
All questions are to be answered.
•
Use a separate answer book for each section.
•
All answers should include explanations in terms of physical principles.
DATA
Free fall acceleration at earth's surface g
=
9.8 m.s-2
42/77(a)
Semester 1, 2004
Page 2 of 6 pages
SECTION A
(Please use a separate book for this section.)
Question 1
In one of the Sports Mechanics laboratory sessions you were asked to study a ball
bouncing off the strings of a tennis racquet. This experiment involved measuring the
height from which the ball is dropped onto the racquet and the height to which it
rebounded. These heights are generally different.
(a)
Using the principles of mechanics, briefly describe why these two heights are
different.
(b)
One way to express the results in the lab experiment used the coefficient of
restitution (COR)
coefficient of restitution =
speed after collision
speed before collision
How would you use the height measurements to estimate the speed of the ball
before and after the ‘collision’ with the racquet strings, and thus calculate the
COR?
(5 marks)
Question 2
Consider a runner in an Olympic 100 m sprint race.
(a)
Sketch a graph of distance versus time for the 10 s it takes the runner to cover
the 100 m during the race.
(b)
Sketch a graph of velocity versus time for the race.
In each case, briefly explain why you have drawn the graph with the shape you have
chosen.
(5 marks)
Question 3
(a)
When catching a hard ball, such as a cricket ball, players will often pull their
hands back while making the catch. How does this help? Explain using concepts
such as velocity, acceleration, force and momentum.
(b)
A baseball player faced with the same problem has the advantage of a large
padded glove. How does this help?
(5 marks)
42/77(a)
Semester 1, 2004
Page 3 of 6 pages
Question 4
A 1500 kg car is travelling north at 10.0 m/s when it is rammed in the rear by a
1000 kg car that was travelling at 20.0 m/s just before the impact. The two cars stick
together and move off together.
(a)
Is momentum conserved in this collision? Why or why not?
(b)
Is energy conserved in this collision? Why or why not?
(b)
At what speed do the two cars move off together?
(5 marks)
Question 5
When a roller skater is spinning around as seen in the diagram, the friction between
her and the ground is very small. As she spins, she moves her arms in and out to
make herself spin faster or slower.
Using the terminology of mechanics, explain how moving her arms allows her to
control her rate of rotation.
(5 marks)
42/77(a)
Semester 1, 2004
Page 4 of 6 pages
SECTION B
(Please use a separate book for this section.)
Question 6
A 60 kg skier starts from rest at the top of a 40 m high hill. She skis down without
using her poles.
40 m
5m
15 m
Sketch the following graphs to illustrate the behaviour of the skier from the time she
leaves the top of the hill (at left) until she reaches the flat at the bottom of the hill (at
right). Ignore air resistance.
Make sure the axes of each graph are correctly labelled. Include values on the graphs
wherever possible.
(a)
(b)
(c)
(d)
(e)
Gravitational Potential Energy of the skier v. time
Total Kinetic Energy of the skier v. time
Total Mechanical Energy of the skier v. time
Velocity of the skier v. time
Acceleration of the skier v. time
(10 marks)
42/77(a)
Semester 1, 2004
Page 5 of 6 pages
Question 7
A plane is flying straight and level 200 m above the water with a speed of 300 km/h.
It drops a package into the water.
(a)
How long does it take the package to hit the water?
(b)
How far away from the target spot in the water should the package be released
in order to land where it is required?
(c)
How fast will the package be moving in the horizontal direction just before it
hits the water?
(d)
How fast will the package be moving in the vertical direction just before it hits
the water?
(e)
What is the total velocity (magnitude and direction) of the package just before it
hits the water?
(10 marks)
Question 8
triceps
biceps
Centre of mass
humerus
ulna
radius
5cm
16cm
34cm
The biceps muscle is connected from the shoulder to the radius bone of the lower
arm at a point 5.0 cm from the elbow, as shown in the diagram. When the biceps
contracts it moves the lower arm.
Take the mass of the hand and lower arm together to be 6% of the total body mass,
acting at the centre of mass of the arm. Assume the force applied by the biceps acts
vertically.
(a)
Draw a diagram treating the arm as a rod. Indicate the forces acting on it and
the position of the pivot.
(b)
Calculate the force exerted by the biceps of a 60 kg person holding a 4.0 kg
sphere.
(10 marks)
42/77(a)
Semester 1, 2004
Page 6 of 6 pages
Answer ONLY ONE of the following parts of Question 9
(a) or (b) or (c). Write no more than 2 pages.
Please note that this question is worth 15 marks.
Question 9
(a)
An Olympic long jump spans ~ 8 m from the take-off point to the landing point
in the sand pit. The jump may be described in terms of different phases (e.g. the
run-up, jumping off the ground, etc.). Discuss the phases of the long jump,
highlighting the different forms of energy of importance during each phase of
the jump.
OR
(b)
A sprint race is started from the blocks with the runners in a crouched position.
In contrast, a long distance race is started from a standing position. Discuss the
differences between these two starting positions in terms of the principles of
mechanics. Why are the different positions used? What advantages and
disadvantages do they offer the runners?
OR
(c)
A tennis shot is hit with ‘top spin’ by hitting ‘over the top’ of the ball as you hit
it in the forward direction. This gives it some spin as indicated in the diagram.
Describe the subsequent motion of the ball – in particular how the ball bounces
off the ground. Explain this motion in terms of forces or other physical
principles. Sketches may help to illustrate your explanation.
Spin of the ball
Direction of motion of the ball
THIS IS THE END OF YOUR QUESTIONS