EDUH SPORTS MECHANICS


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1 4277(a) Semester 2, 2011 Page 1 of 9 THE UNIVERSITY OF SYDNEY EDUH SPORTS MECHANICS NOVEMBER 2011 Time allowed: TWO Hours Total marks: 90 MARKS INSTRUCTIONS All questions are to be answered. Use a separate answer book for each section. Hand in the answers to section A and B separately at the end of the examination. DATA Free fall acceleration at earth's surface g = 9.8 m.s 2
2 4277(a) Semester 2, 2011 Page 2 of 9 Formula Sheet cos! = adjacent hypotenuse sin! = opposite hypotenuse Equations of linear motion Some equations of linear motion have rotational equivalents v = d t a = v f! v i = "v t f! t i "t! = " f # " i = $" t f # t i $t! = " f # " i = $" t f # t i $t! = l r! = v r! = a r v f = v i + at! f =! i + "t d = v i t at 2! = " i t #t 2 v f 2 = v i 2 + 2ad! f 2 =! i 2 + 2"# F gravity = mg F = ma F f ( max) = µf N W = Fd cos! PE gravitational = mgh! = I"! = Fd I = mr 2 KE = 1 2 mv2 KE rotational = 1 2 I! 2 F =!kd PE elastic = 1 2 kd 2 p = mv J = Ft COR = v 2 v 1
3 4277(a) Semester 2, 2011 Page 3 of 9 SECTION A (Please use a separate book for this section.) Question 1 In one of the Sports Mechanics laboratory sessions you were asked to calculate the duration of contact of a basketball with the ground during a bounce off the ground. This experiment involved two sets of measurements: measuring the height from which the ball was dropped and the height to which it rebounded, and measuring the force required to match the observed maximum deformation of the ball. Briefly explain (using equations if you wish): (a) how to use the height measurements to estimate the momentum of the ball before and after the collision with the ground. (b) how to combine the momentum measurements with the force measurement to estimate the duration of contact with the ground. Question 2 The picture shows an basketball player changing direction as he runs down the court. (a) Sketch a diagram showing all the forces acting on him in the position shown in the picture. (b) Why does he push off his foot like this to change direction? (c) Do any of the forces change when he tries to change direction more quickly? Explain why or why not.
4 4277(a) Semester 2, 2011 Page 4 of 9 Question 3 (a) You use a force plate to measure the forces when a person jumps vertically, as shown below. Sketch a graph of vertical force vs time as measured by the force plate. Briefly explain the main features of your graph. (b) The same person now stands on the force plate and jumps higher. Sketch a new graph of force vs time and explain the differences from your sketch in (a). Question 4 A tightrope walker usually carries a long pole to help him maintain balance when walking along a wire. You do something similar when you put your arms out sideways in walking along a fence rail or any very narrow path. (a) With the aid of a simple sketch and concepts such as force, torque, centre of gravity and moment of inertia, briefly explain why it is easy to fall sideways off a wire. (b) Explain why the tightrope walker carries a long pole to avoid falling. (Hint: using the concept of moment of inertia will help)
5 4277(a) Semester 2, 2011 Page 5 of 9 The diagram at left shows a plot of stress v. strain for the biologically important structural proteins Elastin and Collagen. Elastin is reinforced by collagen in the walls of arteries such as the aorta. (a) Define the terms stress and strain as used in this context. (b) Briefly compare and contrast what the Elastin and Collagen curves tell you about the behaviour of these materials. Question 5 (c) Why do you think these properties are useful in the walls of the aorta?
6 4277(a) Semester 2, 2011 Page 6 of 9 Question 6 SECTION B (Please use a separate book for this section.) The displacement versus time graph below shows the motion of a model train, which has a mass of 1.0 kg (a) Briefly describe the train s motion in words, using terms such as displacement and velocity. (b) What was the velocity of the train at t = 8s? (c) What was the train s maximum speed? When did this occur? (d) Sketch the following graphs which also illustrate the train s motion. Make sure the axes of the graph are correctly labelled, with numerical values. (i) (ii) Velocity vs time Kinetic energy vs time (10 marks)
7 4277(a) Semester 2, 2011 Page 7 of 9 Question 7 The following picture shows a water slide. Riders start at the top at rest and let themselves slide down the long ramp. (We can ignore friction between the rider and the slide). At the bottom there is a slight curve so riders leave the slide moving horizontally. L = 6.0 m θ = 45 h = 0.60 m (a) A 75 kg rider slides down the slide. Draw a sketch of all the forces acting on him as he slides down the straight part of the slide. (b) Calculate the net force acting on the rider as he slides. (c) Calculate his acceleration as he slides. (d) What is his speed when he reaches the end of the straight section of the slide? (e) Describe briefly in words what happens when he leaves the end of the slide. (f) If a lighter rider, with m = 50 kg, slides down, how does their speed at the bottom of the ramp compare? (10 marks)
8 4277(a) Semester 2, 2011 Page 8 of 9 Question 8 The picture at right shows a female dancer spinning around in a pirouette. Experienced female dancers usually perform this manoeuvre en pointe in a shoe with a hard, rounded block in the toe. This helps to minimise the friction between the foot and the floor. (a) With her arms spread out and one leg bent she spins with an angular speed of 1 rotation per second. Straightening her leg and pulling her arms in tightly to her body increases her angular speed to 3 rotations per second. Briefly explain why this happens. (b) Starting with this new speed, she allows her rotation to slow back to 1 rotation per second simply because of friction between her shoe and the floor. Her angular deceleration is 0.4 rotations/s 2. (i) (ii) Calculate how long it takes her to slow back to 1 rotation per second. Calculate how many rotations she completes in slowing back to 1 rotation per second. (Hint: use the rotational versions of the three equations of motion under constant acceleration). (10 marks)
9 4277(a) Semester 2, 2011 Page 9 of 9 Please note that Question 9 is worth 15 marks Question 9 In archery a flexible bow is used to fire an arrow towards a target. Assuming the arrow is fired horizontally, explain the mechanics behind the motion of the bow and arrow by answering the following questions: (a) (b) (c) Draw a force diagram illustrating forces on the arrow and the string of the bow when the bow is fully stretched (as shown). Make sure you include all relevant forces. In terms of physical principles, describe the motion of the arrow after it is released by the archer until it leaves the bow. Describe the forms of energy involved with the archer, the bow and the arrow during the firing of an arrow from the moment the archer begins to stretch the bow until after the arrow hits the target. (15 marks)
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