Question

A crane is made from a uniform rigid boom of length L = 30m and weight w = 400N. The boom is sup- ported by a frictionless hinge at its lower end. Its upper end is attached to a support cable which is fas- tened behind the boom at the same horizontal level as the hinge. Adjusting the length of the support / cable adjusts the angle of the boom. In a particu- 7/TTI IN lar application, the crane is used to support a crate with weight W = 2,000N. The boom makes an an- gle 0 = 45° with the horizontal and the support cable makes an angle horizontal NI ITTITTI = 30° with the a) Draw an extended free body diagram (not for a point mass) for the boom showing all the forces acting on the boom. Be sure to indicate the point of application of the force and be sure to label all the forces. (6 points) b) Determine the tension in the support cable. (7 points) c) Determine the horizontal and vertical components of the force exerted by the hinge on the boom. (6 points) d) As mentioned, the support cable can be lengthened or shortened to change the angle of the boom. Suppose the boom is lowered towards the horizontal by lengthening the cable. Explain why you expect the crane to eventually fail as the boom nears the horizontal. (6 points)

Answer 1

The solution of the problem is given below

Page No. Date solution Given w=400N, load W = 2000N crate) F.B.D of boom L= 3om 0-45° 6230. V 450 Ne - T tension force by cable we werght of boom, u Nx & my horizontal & vertical hinge forces The boom is in rotationl equilibrium - . net = 0 Let us take torques about the hinge - Toque due to hinge fore &-a Torque to w to Z2 = ( x 2 caso o cw Torgne due to tension in vertical part of Calle I Zz = LT Cosa sa aw IT other - Torque due to support cake from side - ZynLT Simo-6) Acw..

1 F.B.D for chate & W - .: T=W ccrale is in equilibriu) - T2 2000N showing forces on boom on coordinate axis syslen ny (from figure - A Ny for past (a) co BT o Nr. 7 te For equilibon N = T cos75 Raxis) 2000 x 0.2459 Nr. 518 N right) N - wt J + T singo - 400 + 2000 + 2000 X 0.966 Ny z 4332 Cupwards) - (yaxs) (d) If one considers the rotation of boom about the hinge then & U hinges forces don't contabute in o the torque i Vertical cable tension tries to

Page No. Date TM route the boom clockwise alij Weight of boom also tries to rotate the - boom clockwise in support calce tries to rotate the boom con anti clockwise . The support cable prevents the fallen of boom. Incore the boom is horizontal the torneby support cabe will be zero ie. it will not be able to provide the belancing torque.