STEINGS 43 



Generally the weight- of a string is very slight compared with 

 the other weights in the problem. It is therefore convenient to 

 regard a string as having no weight at all. In this case there are 

 only two forces acting on the particle AB, so that for equilibrium 

 these must be equal and opposite. 



36. Flexibility. A string is said to be perfectly flexible when 

 the force exerted by one particle on the next is in the direction 

 . Thus, if the string now under discussion 



is perfectly flexible and weightless, the forces acting on the parti- 

 cle BC are along the directions pq, qr. To hold BC in equilibrium 

 these must be equal in magnitude. Let T be taken as the magni- 

 tude of each. Also the two forces must be in opposite directions, 

 so that pqr must be a straight line. 



Since action and reaction, by the third law, are equal and oppo- 

 site, the force exerted by BC on CD must also be Tin the direc- 

 tion qr. This must, for equilibrium, be equal and opposite to the 

 force exerted by DE on CD. This force must accordingly be of 

 amount T, and qrs must be a straight line. 



We can continue in this way, and find that all the particles 

 must lie in a straight line pqrs -, and that each acts on the next 

 with the same force T. Also the particle A at the end of the string 

 acts on P with this same force T in the direction of the string. 

 The force T is called the tension. Thus we have the following : 



The tension of a string at any point P is defined as the force 

 with which the particle of the string on the one side of P acts on 

 the particle on the other side of P. 



The tension is the same in magnitude and direction at every point 

 of a perfectly flexible, weightless string acted on by no external forces. 



Hence it follows that 



A perfectly flexible, weightless string acted on ~by no external 

 forces must ~be in a straight line when in equilibrium. 



If the tension vanishes, there is equilibrium whatever the direc- 

 tion of the elements of length pq, qr, . When the tension van- 

 ishes the string is said to be unstretched. Clearly an unstretched 

 string can rest in equilibrium in any shape. 



