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Virtual Work and Static Equilibrium
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[QUOTE="TSny, post: 6642035, member: 229090"] You can make your equations more readable if you use some of the tools available on the toolbar at the top of the posting window. For example: [ATTACH type="full" alt="1655176471155.png"]302790[/ATTACH] Here is my attempt at reformating your equations: (1) dW = W[SUB]1[/SUB] cos30 dx cos0 + W[SUB]B[/SUB] cos45 dx cos180 = 0 (2) dW = W[SUB]1[/SUB] sin30 dh[SUB]1[/SUB] cos0 + W[SUB]A[/SUB] dh[SUB]A[/SUB] cos180 + W[SUB]B[/SUB] dh[SUB]B[/SUB] cos180 = 0 Please correct these if they do not represent what you intended. Also, you should always define the symbols that you use. In particular, what do the quantities dx, dh[SUB]1[/SUB], dh[SUB]A[/SUB], and dh[SUB]B[/SUB] represent? Your second equation looks odd to me. Consider the first term on the right side. If dh[SUB]1[/SUB] is how far the 1 kg mass moves downward, then shouldn't the work done by gravity on this mass be W[SUB]1[/SUB]⋅dh[SUB]1[/SUB]⋅cos0 instead of W[SUB]1[/SUB]⋅sin30⋅dh[SUB]1[/SUB]⋅cos0? Why do you have a factor of sin30? Feynman introduces the principle of virtual work in chapter 4 of volume 1 of the lectures. This is well before he discusses Newton's laws of motion in chapter 9. So this problem is probably meant to go with chapter 4. The principle of virtual work will yield the answer without having to use the idea of "net force equals zero for static equilibrium". You need to be clear on what you are taking to be your virtual displacement(s) for the principle of virtual work. You have two unknowns (W[SUB]A[/SUB] and W[SUB]B[/SUB]). You will need two independent equations. You can get these by imagining two independent virtual displacements of the system. There are several possibilities. For example, if you want to use the principle of virtual work to get your equation (1), consider a virtual, horizontal displacement dx of the knot where the three strings meet. For a particular virtual displacement of the system, the three displacements dh[SUB]1[/SUB], dh[SUB]A[/SUB], and dh[SUB]B[/SUB] can be related by geometry and trig. [/QUOTE]
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