What Weight Should Be Hung at Point P for Horizontal String?

[ritwik06]

Homework Statement

http://img134.imageshack.us/img134/781/86393071cs1.jpg
The figure shows a string with its ends attached to a wall. What weight should be hung at point p so that the lower part of this string becomes completely horizontal?

The Attempt at a Solution

I don't think the string can be horizontal.
I drew the FBD for point p.
since tension is same throughout.
the horizontal part of the string applies t $$\hat{i}$$
the weight applies -w $$\hat{j}$$
the upper part of the string applies -t sin x $$\hat{i}$$ +t cos x $$\hat{j}$$

where x is the angle made by the upper part of the string with the vertical.
Point p cannot be in equilibrium whatever the magnitude of w be.
Am I right?

 

[nvn]

ritwik06: No, point P is in static equilibrium, unless it is accelerating. Were properties for the string given? Tension is not the same throughout the string if a tangential force component is applied in the middle of the string, by an object that is not allowed to slip or roll, right? If the string elongates greatly under the applied load, couldn't the lower segment of the string become horizontal? Try it again.

 

[thomate1]

Your attempt at a solution is correct. Point P cannot be in equilibrium because the forces acting on it are not balanced. The horizontal component of tension from the upper part of the string is always greater than the weight hanging at point P, so the string will always be at an angle and cannot be completely horizontal.