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| course_planning:183_projects:s20_project_11_hidden [2020/03/27 13:49] – created pwirving | course_planning:183_projects:s20_project_11_hidden [2020/03/27 13:50] (current) – pwirving |
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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. | [[course_planning:183_projects:S16 Project 12|Spring 2016 Project 12]] |
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| Following through with it, we have $$\sum\tau_{z}=\tau_{T}-\tau_{g}=0,$$ where $\tau_{T}=hT\sin\theta$ is the torque generated by the tension force and $\tau_{g}=\frac{L}{2}\mathcal{M}g$ is the torque generated by the weights. Now, using the fact that $\sin\theta=\frac{H}{\sqrt{h^{2}+H^{2}}}$ and a little bit of algebra, we can find: $$h=\frac{L\mathcal{M}gH}{\sqrt{4\sigma^{2}\pi^{2}r^{4}H^{2}-L^{2}\mathcal{M}^{2}g^{2}}}.$$ | <WRAP info> |
| | ==== Project 12: Learning goals ==== |
| | * Generate free body diagrams for single-particle systems where the momentum is not changing (statics & uniform motion) to explain the motion of the system and/or to predict various physical quantities associated with the system. |
| | * Generate free-body diagrams for systems subject to tension, compression, and friction forces to explain and/or predict the motion of those systems. |
| | * Collect, analyze, and evaluate data to determine the properties of materials and to evaluate when linear models for those materials become insufficient to explain the data (e.g., Young’s modulus). |
| | </WRAP> |
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| Using our maximum stress of $\sigma_{\rm max}\approx 0.44\times 10^{9}\,{\rm Pa}$ (therefore the maximum tension) we can find the minimum distance $h_{\rm min}\approx 0.47\,{\rm m}$. 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. | <WRAP info> |
| | ==== Project 12: Learning issues ==== |
| | * Static situations |
| | * Relation between torque and force |
| | * Reaction forces |
| | * Using graphs to explain/understand phenomena |
| | </WRAP> |
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| | Your team has been hired to oversee the hanging of a new marquee outside the historic Alamo Drafthouse cinema in Austin, TX. The design calls for the marquee (mass, $200\,{\rm kg}$) to hang from the middle of a steel pole (length, $2.5\,{\rm m}$; mass, $1000\,{\rm kg}$). The pole has one end bolted to the outside of the building and is positioned horizontally. There is a hook from which your team may connect a steel cable (diameter, $1\,{\rm cm}$) to the pole for additional support; hanging the marquee to the pole alone will damage the exterior of the historic building. A hook exists at a height $1\,{\rm m}$ from where the pole would connect to the building. Your team needs to determine if the steel cable you were shipped (stress-strain data shown below) can be used to support this marquee (and where precisely you can hook the cable to the pole). The Greater Austin Historical Society will only allow you to use the existing mount on the exterior of the building. You should also check that the reaction force perpendicular to the wall due to the steel pole doesn't exceed $30,000\,{\rm N}$ because if it does it will punch through the exterior of the building. |
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| | {{url>https://plot.ly/~PERLatMSU/17.embed 640px,480px | Stress-strain curve for Metal Alloy}} |