Question

The prism in Figure 98 has a width, w = 1.5 in, a height, h = 1 in., and a depth, d - 2.5 in. Pl is a force along line FO and has a magnitude of 4.1 lb. P2 is a force along line BG and has a magnitude of 6.2 lb. What is the magnitude of the total moment about line AG? A W

Additionally, for the prism described above, what is the magnitude of the moment about line OG and what is the magnitude of the moment about line BF?

Answer 1

The magnitude of the total moment about line AG = 1.99 lb-in

The magnitude of moment about line OG = 0

The magnitude of moment about line BF = 0

The magnitude of moment produced by force. B about lime AG will be zero because the line of aclion of force pe hasses through home a which lines on line AG. Therefore we only have to calcaulate the moment of force Pi. about line AG. W=15. B Th=lin Id=2.5 in 32 • Write position vector of point A and Gi 60 = :5ê 2.5Ê Here to and Go are position vector of point A and G respectively. ÁG = AO - GO Here AG is vector from point G to hoint A i.e. vector along line AG. | BuzukƯo. - 1 and a = (-55 2-5k . AĞ = ĝ – (1-5ô + 2.58). AG = -1050 +3 - 25

JAGI Here Vaca is wret vector along AG and InG) is magnitude of AG Suleslitult AG = -10 5ê +4- 2.5K and WG le 1152 + +2.52 Uno = -105ê + 9 - 25R 1052 #12 +052 tha = -1.50 +1 -2.5k 105 ŏ o Cross Product then = -l. 5î -© Here üp is momond arm of force Pry about froint G. Ñ - 4.1 - 0. Her Pi is cartesian vector form of forp,. • Calculation of moment generated by P about hoint G : M = p XP Substitute for = - 15 i and Pi= -folk from equation and Mo = (-1-5W) x(+4-1ť) . î Â I 0 0 -41 Mo = - ] (1.5x4.1) Mo = 66-159) lb-in. —- • Calculation of component of Mo along line AG. MAG = . Mis MAG Here MAG is compoment of Mo along AG Substitute Mo = -615] ) lb-in and more on AG = -105 t - 25k. 99.5 in above equation, Mas = 6-6-159).(-lišáth 2:53) -- 616X Dot Proclucl MAG= -1.99 lb-in 19.5 19.5 Cotal momond about line AG= IMaul = 4.99db-in

Calculation of Magnitude of Moment about line 06: The moment produced luý , about line 06 is gero because the line of action of force Pr passes through hoint o which is on line OG The moment hevoduced by Pz about line OG is zero because the line of action of force P2 frasses through hont G which lies on line OG Therefore moment of force P and Pz aluout line OG is zero Magnetude of moment aloud line OG = 0 • Calculation of Magnitude of Moment about line BF: The moment produced ley Pi about line BF is zero because the leve of action of a hasses through hoint F which is on line BET The momeno hrodused loy Pa about line BF is zero because the line of action of P2 hasses through the point B which is on line BF. Therefore moment of force Pi and P2 about line BF is zero Magritude of moment about line BF =0 /