Question

4. Six forces, each of magnitude either For 2 F. are applied to a door as shown. Find the six torques about the hinge T, through to and rank in order, from smallest to largest. T -0 &t=mir, tmzz... 1/4 L/ 4 LL/4 L/4 To 2F 2F is I(-)

Answer 1

Zal 뉴뉴뉴카뷰 F 2 F us we know that Zai CYKF a Ž =18 hi sino ñ where of is vector of point of application of force from, about which, we want to - point Calonlente torque o is angle between 3 and ñ is unit perpendicular rector to plane containing go and Now, calculating torque 17= F sim go' Hinge 26 a = 5(25) (ø) = LFLR)

(131 = b Esimo e din - Fsing abes F Coso in Horizontal component of force (I caso) does not produce any - torque - THOVE Fsino - 90 121= (F simo) R - Fsino (8D 2- (-Flosa) t -> 2F =22 singo With = 2LF_simeo 1 2 = 2 (2f) singo (Åf any = 22F (6) --F--# - > -- > LF simo 0 0 (vi) Zd=LF sino ŽELF simo o l z = 0 m angle between force and ŷ is o So, no torque will produce ce:

thease tosques from smallest to we want to rank 1 largest 50, we con see from above Calenlations that the correct rank for torques is 17642 = 24 <c, =C₂ <ts this is the required sank.