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Homework Statement
The system shown in Fig. 2-6 is in static equilibrium. Use the principle of virtual work to find the weights A and B. Neglect the weight of the strings and the friction in the pulleys.
Homework Equations
Conservation of gravitational potential energy.
The Attempt at a Solution
The system is in static equilibrium so the weights may be moved without changing the energy of the system. Consider weight A moving down by 1m (lets pretend this is a 'small distance' for the purposes of virtual work). Then by some geometry we find the 1kg weight moves up by [tex]\frac{1}{sin(30)}[/tex] m and weight B moves by [tex]\frac{1}{sin(45)}[/tex] m. By equating GPE,
[tex]A = \frac{1}{sin(30)} + \frac{B}{sin(45)}[/tex]
For two unknowns we need two equations, but moving the other weights an amount just gives back the same one. I am unsure how to create a second equation.
Note: This problem is simple enough using forces but that is not the method asked for and I would like to improve my ability at using this method.
Thanks for your help!
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