A man of mass 74.4 kg stands on a scaffold supported by a vertical rope at each end. The scaffold has a mass of 21.9 kg and is 3.9 m long. Suppose the man stands to the right from the middle of the scaffold that is a distance one sixth of the length of the scaffold. What is the tension in the right rope? b) What is the tension in the left rope? thanks in advance.
this could be a 2d concern. The moments approximately any factor interior the gadget would desire to stability, in the different case the gadget (scaffold) would rotate. additionally, the vertical forces would desire to stability, or the gadget (scaffold) would translate. it form of feels to me that to the superb from the middle of the scaffold it somewhat is a distance one 6th of the dimensions of the scaffold is comparable to saying 2-thirds from the left-edge of the scaffold. The moments could be summed approximately any factor. i will evaluate the left facet of the scaffold, the place the 2d produced by the left rope is 0. comprehensive M = 0 = scaffold M + guy M + suited rope M 0 = 23.7kg*9.8m/s^2*(3.1m/2) + 60.1kg*9.8m/s^2*(2*3.1m/3) - F*3.1m wherein: the scaffold is considered a factor mass located at its center the strain F acts opposite to the load of the guy and the scaffolding, and subsequently has -ve sign remedy for F. To get the strain in the different rope, you are able to basically evaluate the vertical forces interior the gadget. on the different hand, you should sum the moments approximately another factor (say, the superb rope). wish this permits.
Left rope = T1 Right rope = T2 1/6 of 3.9 m = 0.65 m 3.9/2= 1.95 1.95 - 0.65 = 1.3 m from right rope. Take g = 10m/s^2 T1 = ((219 x 3.9)/2) + (744 x 1.3) = 1394.25 1394.25 = 3.9 x T1 1394.25/3.9 = T1 = 357.5 N (answer for left rope) T2 = ((219 x 3.9)/2) + (744 x (3.9 -1.3)) = 2361.45 2361.45 = 3.9 x T2 2361.45/3.9 = T2 = 605.5 N (answer for right rope)
