Proving tension in rope of equilibrium system

[Qwertywerty]

Haruspex , I was wondering - the fact that balancing torques about point X gives us a single equation is all well and good - but does it necessarily give you a faster solution than say , about point O ?

 

[SammyS]

For this problem, I like finding the torque about point O. Using point X is also handy. In this problem, the unknown distances OC and BC make any method using them fairly complicated, whereas the normal forces (especially N_A) are not too difficult to work with.

If the student understands how to use the line of action of a force, then using point X does give a nice result. But using the "line of action" also makes point O and even point B good points for evaluating the torque.

SammyS

 

[andrewkirk]

If one uses torques about O, T does not come into the equation because it does not provide any torque about O. So one would need to use additional equations to solve for T.

 

[SammyS]

If one uses torques about O, T does not come into the equation because it does not provide any torque about O. So one would need to use additional equations to solve for T.

Sure, but T comes back in by considering the forces equation(s).

 

[Qwertywerty]

Sure, but T comes back in by considering the forces equation(s).

Yes , I think he has mentioned that you would need additional equations .

Haruspex , I was wondering - the fact that balancing torques about point X gives us a single equation is all well and good - but does it necessarily give you a faster solution than say , about point O ?

What I was trying to say here was that although you would get more equations , time would not be much of a factor , as the three equations required to be solved while using O could be , easily and fast .

 

[haruspex]

What I was trying to say here was that although you would get more equations , time would not be much of a factor , as the three equations required to be solved while using O could be , easily and fast .

If the other two tricks do not come immediately to mind, I agree there would be no time saved in the problem in this thread. However, it is a useful option to look for in general.