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Old Jul 24th 2009, 01:25 AM   #1
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Unhappy Too many variables




A verticle force $\displaystyle P=50N$ is applied to the ends of the $\displaystyle 0.6m$ cord AB and spring AC.

If the spring has an unstretched length of $\displaystyle 0.6m$, determine the angle $\displaystyle \theta$ for equilibrium.

Take $\displaystyle k=250Nm^{-1}$


I have try to resolve them and sum of F = 0,
but there are too many variables,
I cant solve it.
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Old Jul 24th 2009, 09:10 AM   #2
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Problem doesn't seem solvable. Insufficient data. Is the angle made by the spring and the cord specified?
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Old Jul 25th 2009, 09:52 AM   #3
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Originally Posted by Akshay View Post
Problem doesn't seem solvable. Insufficient data. Is the angle made by the spring and the cord specified?
No, it has not been given.
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Old Jul 25th 2009, 04:07 PM   #4
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Too many variables

SengNee,

The problem is solvable, you can use the 1st differential of the change in potential energy of the system. As the mass lowers, the gravitational potential energy is stored as elastic energy in the spring. Express both the gravitational energy and the spring energy as a function of theta using the geometry of the problem.

Alternatively, you can use the force generated in the spring as it changed length (use the cosine rule), determine the vertical component of the force, subtract this from 50 to get the vertical force component of the cord. Work out the horizontal components of the cord and the spring and where the two are equal, that is where the balance point sits.

You will have to use a method such as the newton raphson method to solve the resulting equations as I am not really sure how you would solve them by elementary means.
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Old Oct 13th 2009, 10:36 PM   #5
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I know this.
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