Question

Problem 8 (Bicep workout) We can estimate the tension on the bicep muscle while lifting a weight with our hand. In this exercise, the lower arm pivots about the elbow (assumed fixed), while the bicep itself is attached to the lower arm 4 cm away from the elbow (see drawings below). The weight (W) has a mass of 10 kg and is assumed to be a point mass for simplicity which exerting a force on the arm. The lower arm itself is modeled as a uniform rod with mass 8 kg and length 26 cm (from 0 to the center of the object) fr 26 cm 4 cm 58S 14 cm For all questions below, torques are measured relative to the origin (0) and counterclockwise rotations are positive. A. What is the moment of inertia of the weight about an axis running through the origin (O)? Use units of kg.mand round to the first decimal place. Assume the weight is 26 cm away from the origin O. B. What is the moment of inertia of the lower arm about the same axis as in question A? Use units of kgm and round to the nearest second decimal place. C. What is the total moment of inertia of the flower arm + sphere) system about the same axis as question B? Use units of kg m and round to the nearest second decimal place.

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Answer 1

R Answer: - 126 cm - |(4cm,o) (26 cm, o) (14 cm,o) ca ----->te 31 J EW-A is 14cm -> via = 8g clog A Moment of merfia of weight origin o=? 1,- (moss of weight) ( Perpendicular distance of origine -(10)(26x10-2) I, = 6760 x 10-4 kg.me i. I, = 0.7 kg m 2 ③ moment of merfia of arm about origin 12 = (mass of arm) (perpendicular distance of contre of mass) gravity of arm from origin 7 - (8) (14 X10-2)2 - 8x196x1004 Reg.ma 12 = 1568x10-4 kegime .. I2 = 0.2 kg = m2 © Moment of ineofia of (lower arm +Sphere) abouf origin I - I, +12 20.6760 kg.m2 +0,1568 kg.m2 20.8328 kgima ;.I - 0.83 kq.ma 1 1 P

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