Exam2Pr2 - % % Alternate approach for students who didn't...

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Sheet1 Page 1 % Exam 2, Problem 2 % Unit vector N> points to the right % % Set up problem OVERWRITE ON FRAMES N BODIES D,E,F POINTS P,Q,R CONSTANTS LD,LE,LF,B CONSTANTS THETA,PHI MASS D=MD,E=ME,F=MF % % Mass center in N> direction % SUM(Mi*P_O_Qi>) % P_O_CM> = ----------------- = 0> % SUM(Mi) % if we take O to be on the line H-H. P_P_DO=-(B-0.5)*LD*SIN(PHI) P_P_EO=0.5*LE*SIN(THETA) ZERO[1]=EXPLICIT(MD*P_P_DO+ME*P_P_EO) % % Law of sines to eliminate sin(phi) ZERO[1]=REPLACE(ZERO[1],SIN(PHI)=(2*LE/LD)*SIN(THETA)) SOLVE(ZERO,B)
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Unformatted text preview: % % Alternate approach for students who didn't realize % that we only care about the horizontal direction. % Let N1> point to the right and N2> point upward. % P_P_DO>=(B-0.5)*LD*(-SIN(PHI)*N1>-COS(PHI)*N2>) P_P_EO>=0.5*LD*(SIN(PHI)*N1>+COS(PHI)*N2>)+0.5*LE*(-SIN(THETA)*N1>+COS(THETA)*N2>) POINTS CM P_P_CM>=(MD*P_P_DO>+ME*P_P_EO>+MF*0>)/(MD+ME+MF) ZERO[1]=DOT(P_P_CM>,N1>) ZERO[1]=REPLACE(ZERO[1],SIN(PHI)=(2*LE/LD)*SIN(THETA)) SOLVE(ZERO,B) % B = 0.5 + 0.25*ME/MD...
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