Question

Two rigid rods as shown, AB and BC are connected to a pivot (A) and initially at rest as shown. Each rod has mass of 3 kg and length L = 0.5 m. A force P as shown is then applied to rod BC at some distance b from B (the pivot between bars A and B). Please find the distance b where, when force P is applied, the two rods (AB and BC) move together as if they formed a single rigid body of length 2L. (Hint: think about what it means for both bars to move together as a rigid body)

Answer 1

Dear student

Answer summary

b = 0.22827 m = 227.27 mm

Please pay attention to the kinetic diagram details.

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Froee body diagram Enteral forces and internal reactions Kinetic dicqarum This diagram include accelcrcation toom (man) and rotational inestal term (1 o) at center of man. Consider ABC a s a single rod. Consider ABC .--2A La An Tags La ster of mass mass center >mas Hala Nc linear accelasution, q= o x angulcu acceleration r=L a= La Cacts at center of mass) Free body cliagram (with external load + reactions at Support) = Kinetic dicigram with accelaration and rotational inertia at mass center.

Free body diagrams um troms Kinetic clicgrom terms. ma and Ia at mass center Getermal force acting on body = Sinsilarly Moment of enternal force about a Moment of the accelarcition and rotational interatia teroms.

Free body diagrams um troms Kinetic clicgrom terms. ma and Ia at mass center Getermal force acting on body = Sinsilarly Moment of enternal force about a Moment of the accelarcition and rotational interatia teroms.

before calculating moment determine Mass, length, Qq and I total mass = m+m = 2m total lengthy'= 24 MI of rod ML2 2mx (@L? about CG = T - 12 Moment cum op max = L. P = maxt I a POL+b) = man L + Ia take moment about A. P (L+b) = 2m (Lx)* L + P (L+5) = 2m22a + 2ppa 3 P(L+b) = 8 2² ma Unknow-a = to consider BC- douw find a FBD q kinetic diagram.

FBO of BC Kinetic diagram со всеми Cloud + veaction) (max+ I.) ł acts at CG Before starting calculation we have to find an (which acts at CG of BC) azra 8= 3L An= 3 La > Apes are FBD Kinetic diagoon a B B Bn ca ---> max TIL P = mant la

take moment about B Dx b = m Anex I + Ia - I = M2 au = 3 La Pb = mx 2 x x + 2 + M1L2 2 2 Pb = 3 Pb = q (Ma) intems of Ph yuz a we got a - Pin and Substitute in equation ④ PCL tb) = 2/3 [mx & PCL+b) = 16 Pb PL + Pb= loob - L+b= 16 lb

1-15b-b 녀b 야유 L = 0.5m b = 1x05 = 22721) b=227.27mm) Answer.