Question

Question 2 In the figure, a package of mass m hangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at angle o = 31.9° with the horizontal; cord 2 is at angle e. (a) For what value of e is the tension in cord 2 minimized? (b) What is the ratio of the minimum tension in cord 2 to the weight of the package? (a) Number Units (b) Number Units

Answer 1

Q = Ti sind +T, Sine 31.90 Ti Tz o = we have to minimise it 6 I, cosa Izcoso ca) mg For equilibrium. Efy=0 { fx=0, ET-O In y direction, T, sind + Tz Sino - mg In a-direction, T2COSO - Ticos d = 0 Ti coso = T, - Tz coso => Tacoso coso SO) Tz cose x sind + Tz sino ng coso * Tz (tans &) coso + Tz sino ng mg - Tz (cose tand + Sino) $ = 31.90 SO tan (31.90° - 0622445 mg So, T2 = Cos OxC0-622445) + Sino to minimise Tz, dTz do - O - 0 (coso tan + Sino) xo mg (-Sing tand + coso) close tand + Sino)? - Sino tand -coso tano tane = 1.606567185 tand o = 58.10 (a) (b) T2 = 0.849 mg COS 158.19 0.622445 t Sin (581)