PHYSICS 170 MECHANICS I Final Exam: 8:30 am to 11:00 am, Friday April 20 2018 SOLUTION TO QUESTION 1 page 1 a) Free-body diagram K A Z A 4 m A Z € 10,0, 1)m - - 12 . 10 mx 1 A 10 0,0)m 0 5 An 1 FAC My D(0,20) m F D 14 Q12 B ( - 1,0 ) m 9
PHYSICS 170 MECHANICS I Final Exam: 8:30 am to 11:00 am, Friday April 20 2018 SOLUTION TO QUESTION 1 page 2 b) Cartesian component force equations of equilibrium Forces (suppressing units) F = A ]+ Ak Fpc=(?-2]+k)X F .=- 400?+300]+200k F =- 900 k Force equations of equilibrium ?F =0: x X=F /V12+22+12 BC X-400 = 0 (1) ?F =0: y A-2X+300 = 0 (2) ?F=0: A + X +200-900 = 0 Z Z (3)
PHYSICS 170 MECHANICS I Final Exam: 8:30 am to 11:00 am, Friday April 20 2018 SOLUTION TO QUESTION 1 page 3 c) Vector moment equation of equilibrium (about point A) Couple moments (suppressing units) M =M?+M ]+M? M=500? +100]+ 400k Moment equation of equilibrium (?.) =?? + ?(F x F) =M?+M ]+Mk + 500? +100}+ 400k i j + 10 0 X -2X i j 1| + -1 2 X -400 300 1. j 0+02 0 |=0 200 0 0 -900 d) Cartesian component moment equations of equilibrium (about point A) ?? =0: x M +500+2X +400-1800 = 0 (4) x ?? =0: y (5) y M +100+X+200=0 ?? =0: M +400-300+800 = 0 2 (6) Z