course_planning:183_projects:s20_project_11_hidden

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The first thing we do, since this is a static situation, is to choose our system, choose the point about which we want to sum the torques, and do it. Our system can be the pipe and the marquee. The point about which we sum our torques can be the point where the pipe connects to the wall – this way, we don't need to know the reaction forces on the wall when we do some torque sum.

Following through with it, we have τz=τTτg=0,

where τT=hTsinθ is the torque generated by the tension force and τg=L2Mg is the torque generated by the weights. Now, using the fact that sinθ=Hh2+H2 and a little bit of algebra, we can find: h=LMgH4σ2π2r4H2L2M2g2.

Using our maximum stress of σmax0.44×109Pa (therefore the maximum tension) we can find the minimum distance hmin0.47m. Any smaller h will result in the cord snapping. This tension carries all the way through the cord to the hook on the wall. Thus, the reaction force on the wall-cord interface is equal and opposite to the tension.

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  • Last modified: 2020/03/27 13:49
  • by pwirving