Laws Of Motion

Laws Of Motion

FUNDAMENATLS OF STRINGS:
1. A string is assumed to be inextensible,i.e., perfectly elastic and massless.
2. The magnitude of accelerations of a number of bodies connected through  stringsis always same.
3. The tension is every part of the string remains the same. This is equal to the applied force.In order to produce tension in the string,two equal and opposite stretching forces must be applied.
4. If the tension is the string is increased continuously ,it breaks down.The maximum tension which a string can bear without breaking is called breaking strength.
5. When a string is fixed horizontally by clamping its free ends and loaded at the middle,as shown in fig.the tension T is given by
                         

It is clear from this expression ,that tension is the string will be lesser,equal or greater than load depending upon the value \(\theta\).
(i) The tension in the string will be minimum where \( \cos \theta = \max .,i.e.,\theta = 0^ \circ \) as shown in figur.
                            
 This shows that the tension should be loaded at the middle can never be lesser than half the suspended load.

(ii) The tension in the string will be maximum when \( \cos \theta = \max .,i.e.,\theta = 90^ \circ \) as shown in figure.
                          
                                        In this case,\( T_{\max } = \infty \)
This situation cannot be realized practically because the string can bear a finite tension while the tension here is infinite.Therefore,a string loaded at middle can never remain horizontal.