A man of mass 64.9 kg stands on a scaffold supported by a vertical rope at each end. The scaffold has a mass of 18.7 kg and is 3.3 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?
take the left end as the hypothetical pivot then CCW torque = CW torque T*3.3 = (m g)_man * 2.2 + (m g)_scaffold * 1.65 3.3T = 2.2(64.9)(9.81) + 1.65(18.7)(9.81) = 1703.36 T = 516 N
that's a 2nd problem. The moments approximately any factor interior the device might desire to stability, in the different case the device (scaffold) might rotate. additionally, the vertical forces might desire to stability, or the device (scaffold) might translate. it form of feels to me that to the appropriate from the middle of the scaffold that's a distance one 6th of the size of the scaffold is comparable to asserting 2-thirds from the left-fringe of the scaffold. The moments may be summed approximately any factor. i will evaluate the left factor of the scaffold, the place the 2nd produced by way of the left rope is 0. entire M = 0 = scaffold M + guy M + appropriate 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 regarded as a factor mass placed at its middle the stress F acts opposite to the load of the guy and the scaffolding, and for this reason has -ve sign resolve for F. To get the stress in the different rope, you are able to basically evaluate the vertical forces interior the device. in spite of the undeniable fact that, you will possibly desire to sum the moments approximately another factor (say, the appropriate rope). desire this facilitates.
A man of mass 64.9 kg stands on a scaffold supported by a vertical rope at each end. The scaffold has a mass of 18.7 kg and is 3.3 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? Man’s weight = 64.9 * 9.8 = 636.02 N Scaffold weight = 18.7 * 9.8 = 183.26 N The distance the left end to the center = 3.3 ÷ 2 = 1.65. The weight of the scaffold is located 1.65 meters from the left end. The distance from the center to the man = 3.3 ÷ 6 = 0.55 m. Distance from left end = 1.65 – 0.55 = 1.1 m So the weight of the man is located 1.1 m the left end. 0 ………. 1.1 ………... 1.65 ………….…….. 3.3 ↑________↓_________ ↓________________ ↑ T left…… 636.02 …… 183.26 …………… T right Left end is pivot point. Clockwise torque = 636.02 * 1.1 + 183.26 * 1.65 Counter clockwise torque = T right * 3.3 Counter clockwise torque = Clockwise torque T right * 3.3 = 636.02 * 1.1 + 183.26 * 1.65 T right = (636.02 * 1.1 + 183.26 * 1.65) ÷ 3.3
