PHYS 170 Worksheet 5.2 Student ID 59718130 Family Name Srivastava 62115070 49713258 Nayapli Bradley First Name Vizith Heydar Jack Email ViJitLos@gmail.com herdarnararli2005@gmail.com jackbrad 4721@gmail.com 1. Find the tensions in cables A and B, and the components of reaction at ball and socket joint D. 1 A. Draw the free body diagram for the strut by adding force vectors Fp, Fc, Fpx, Fpy, and F, A DZ B. Write the coordinates of A, B, C, and D in the xyz coordinate system as column vectors A[! ] DON NWO B [] [] L 1 D[ % ] 000 x C. Write F, as a column vector This B 7 A FDX B DZ z 3 m C 2 m D 0 30° 250 -500 Cos 3. D. Write the force vector F at D as a sum of the unit column vectors ? 1. 0 ? 0 ? ? ? 0 ? 0 ? ? ? ? 500 N i =0 0 0, j =0 1 0, k =0 0 [ times magnitudes Fox , Fpy , and FDz HOH ? 0 ? ? ? 8 1 1 For 1 0 00 ) F. + Py 1 1 0 1 1 1 + F Dz 1 0 1 0 0
E. Write the unit vectors for F and Fc (-6,-3,27 11 L 361977 ~1 6 3 2 140 Fc = ( F. Write the force-balance equations using unit column vectors and F , F , Fpx , Fpy , DY , Fp2 and (8)= FAX( 6 0 + FB (=3 ) 1 + Foy (!) +FDE ( 8 ) 2 + F (°) 54. G. Using D as the reference point, write the moment of F, as a column vector 7 X DA 0 250 ) x (:) -50010530 0 -2598 = - 1500 -6 7 - 3 7 2 3 H. Using D as the reference point, write the moment of FR as a column vector times FR PAX FRES = (%) X 1 1 FB = 0 -1.71428 -2-5714 1 FB
FRA X FC = ( 8 ) x 540 6 I. Using D as the reference point, write the moment of F as a column vector times Fc 0 ) 2 0 1/ 540 Fc 11 -1.897366 0 J. Write the moment balance equation using column vectors and Fp and Fc - 0 0 ) For -2598 | = 0 (-1.89736) Fc +/-1.71428 ~2.5714 1500 0 9 K. Write the augmented matrix for the system by combining the force-balance equation and the moment-balance equation, with an extra line at the top to show which unknown is associated with each column. You will need to add some zeros since Fox , Fry Dy , and FDZ don't appear in the moment balance equation. F FB Fox Fpy FDZ 1 6 0 1 0 0 N 540 -250 -3 0 2 0 1 0 + Suocos30 7 2 7 0 0 0 1 0 0 - 1897 0 0 -