Homework_1_ENGN1210_S24

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1210

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Biology

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Apr 3, 2024

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Page 1 of 3 ENGN 1210 Sp24 Homework #1 Biomechanics (ENGN 1210) Spring 2024, Professor Vikas Srivastava, Brown University Due: Friday, February 2 by 6 p.m. (Online submission) ______________________________________________________. _____ DIRECTIONS: • Write your name on the first page and your initials and page number at the top of every page • Write the names of collaborating students for each problem • Show all work/calculations and assumptions • Box or underline final answers where applicable • Scan and upload your solutions on Gradescope through the canvas as a single pdf file. If you use MATLAB etc., include images of your code as an appendix in the same file • Total score: 100 points Question 1 [10 pts]. Role of biomechanics List 3 examples of how biomechanics plays a vital role in health care. Limit your answer to a maximum of 150 words. Question 2 [5 pts]. Forearm supporting weight Calculate the reaction force and moment at the elbow when a person supports a tray full of drinks in one of his hands. Consider a posture where the arm from shoulder to elbow is parallel to the body and the person is extending his forearm straight outwards parallel to the ground to hold the tray. The tray with the drinks has a mass of 3 kg. The forearm is 36 cm long, and the weight of the forearm and hand is 4.5 N. You can assume that the center of gravity of the forearm and hand is 18 cm from the elbow. Question 3 [10 pts]. A cast leg Figure 1 shows a leg in a cast that is supported by a pulley and weight arrangement. The leg at equilibrium is at a 10° angle to the horizontal. The leg is supported by a mass of 16 kg, which acts on the cast at 20° to the horizontal through a pulley system. Calculate the force in the leg along its axis. Figure 1. Plastered leg support 18 kg 3 kg ø

Page 2 of 3 ENGN 1210 Sp24 Question 4 [25 pts]. Leg mechanics A skeletal diagram of the lower leg is shown in Figure 2. Here, this portion of the leg is lifted by the quadriceps muscle attached to the hip at A and to the patella bone at B. The bone slides freely over cartilage at the knee joint. The quadriceps is further extended and attached to the tibia at C. Using the mechanical system shown in the upper schematic to model the lower leg, determine the tension T in the quadriceps and the magnitude F D of the resultant force at the femur (pin at D) to hold the lower leg in the position shown. The leg with a weight W 1 has a center of gravity at point G 1, and the foot with weight force W 2 has a center of gravity at point G 2 . The schematic shown on the right side of Figure 3 is provided as a hint. Figure 2. Lower leg mechanics Question 5 [25 pts]. A simple truss Find the internal forces in the truss structure (at nodes and in the members) shown in Figure 3. For each member, note whether it is in compression or tension. Figure 3: A representative truss structure y x

Page 3 of 3 ENGN 1210 Sp24 Question 6 [5 pts]. Tennis racket grip During a tennis game, a player hits a volley in which the racket experiences a peak axial force of 180 N. The coefficient of static friction between the racket and the player’s palm is 0.2. How much squeezing pressure (assume uniform pressure around the cylindrical grip) does the player need to apply on the racket handle to avoid slipping? Consider that the racket handle is circular and 40 mm in diameter. Assume the width of the palm to be uniform 70 mm. Question 7 [20 pts]. The heavy nucleus in cell A neuron is pictured in Figure 4. You can see that the center of gravity (marked with a red X in the schematic) of the entire cell body/soma (which includes nucleus and cytoplasm) is 1 micron away from the centroids of the soma. The cellular nucleus is packed full of DNA and has a higher density. Estimate nucleus density ( r N ) in relation to the average density ( r c ) of the cell material outside the nucleus. Assume the neuron lives and acts entirely in a 2D plane. Figure 4. Neuron

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