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It is the homework about medical physics for the student to research and practice.
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Physics 315: Medical Physics - Homework # 1 : Fun with statics Due Tuesday, February 13 th^ at 11:00 AM on paper (1) In the arabesque position on the right an initially upright ballerina kicks one leg backward and upward while keeping it straight (mass mleg), pushes her torso and head forward (mass mtorso+head), and propels her arms backward and forward while keeping them straight (each marm). They, respectively, make acute angles θleg, θtorso+head, and ±θarms, to the horizontal. The centers of mass of the extended leg and vertical balancing leg are xextended-leg and xbalancing-leg behind the vertical from the center of mass (in the midsagittal plane), and that of her upper body (torso/head/arms combination) is xupper-body in front of this vertical (so all of these distances are defined as positive). In achieving this arabesque position her center of mass drops vertically from height ybefore to yafter. (a) Draw a diagram showing the gymnast before and during this maneuver. (b) Find the equilibrium condition in terms of these masses and distances. (Hint: Analyze the torques about her center of mass in the arabesque position.You can ignore the contribution from her arms. Why? You may not need all of the information that is presented.) (c) Assume the gymnast is 1.49m (4 ft 11 in) tall and has a mass of 38 kg (weight 84 lb) and her free leg and arms make a 30◦ angle with the horizontal. What angle does her upper body make with the horizontal? (Assume the anthropometric relations for a standard human.) (2) The distance from your instructor’s elbow to the middle of his hand is 34cm. He has a 25 kg weight in his hand, and his arm and hand together weigh 1.5 kg. His bicep muscle attaches 4cm from his elbow. (a) What minimum force does his bicep muscle have to exert to lift this weight? Be sure to draw a force diagram. (b) Assuming that the bicep muscle does not exert a different force at different lengths, does the angle that the elbow takes affect the minimum force required to lift the weight. Demonstrate your answer. (c) 7 foot 6 inch basketball player Yao Ming’s forearm + half-hand distance is 76 cm. His arm and hand together weigh 2.1 kg. Assuming that his bicep attachment point is still 4cm from the elbow, what force does his muscle have to exert to lift the same weight? How much does this change if his attachment point is 6 cm from his elbow?
( 3 ) A gymnast of mass mb suspends himself on the rings with his body upright and straight arms that are horizontal with which he clutches the rings. Each ring is suspended by a rope with tension T that makes an acute angle θ with his arms, and the rings are separated by a distance d. (a) Solve for the T and θ. Assume symmetry. (b) If the gymnast weighs 600 N, θ = 75◦, and d = 1.8 m, find T. (4) A man has a humerus length of 0.4 m. He weighs 8 5 kg. The Young’s modulus for bone is 179x10^2 MPa. When he does a pushup, his humerus shortens by 0.03 mm. The ultimate compressive stress (UCS) for bone is 170 N/mm^2. (a) Diagram the structural makeup of bone. What are its molecular components? (b) What is the diameter of his humerus? (c) How long is his humerus when he does a one-armed pushup? (d) What fraction of the UCS does the answer in part C represent? (e) Assuming that no other part of his body breaks down, how much can he weigh and still do a one-armed pushup without his humorus exploding? (5) A 75 kg man has a 2 50 mm long Achilles tendon. During running, the peak force on his tendon is 5 5 00 N. His tendon has a cross-sectional radius of 90 mm^2. The ultimate tensile strength (UTS) for this tendon is 100 MPa. (a) Diagram the stress-strain diagram for a tendon. Label the important parts. (a) What is the stress on this tendon in MPa? (b) How much longer does it get? (c) How much energy gets stored in this tendon at the moment of peak force? (d) Assuming that the peak force is linearly proportional to body weight, what is the maximum that the man can weigh and run without snapping his Achilles?