STRINGS 45 



Although Hooke discovered this law in 1660, he did not publish it until 

 1676, and then only in the form of the anagram ceiinosssttuv. 



In 1678 he explained that the letters of the anagram were those of the 

 Latin words ut tensio sic vis, "the power of any spring is in the same 

 proportion with the tension thereof." By tension (tensio} Hooke meant 

 the quantity which we have called the " extension "; by the power (vis) 

 he meant the force tending to stretch the spring, i.e. the tension. 



39. Hooke's law only enables us to compare the extensions 

 produced by different tensions. To find the actual extension pro- 

 duced by a given tension we must know that produced by some 

 other tension for comparison. 



DEFINITION. The force required to stretch a string to double its 

 natural length is called the modulus of elasticity of the string. 



Thus if a is the natural length of a string, and X the modulus 

 of elasticity, we know that a tension X produces an extension a, 

 so that a tension T produces an extension Ta/\ 



When we say that a string is inextensible, we mean that X is so 

 large that the extension Ta/\ may be neglected. 



Hooke's law only holds within certain limits. If we go on 

 increasing the tension in a string indefinitely, we find that, after a 

 certain limit is passed, Hooke's law ceases to be true, and when a 

 certain still greater tension is reached the string breaks in two 

 parts. 



EXAMPLES 



1. A weight W hangs by a string and is pushed aside by a horizontal force 

 until the string makes an angle of 45 with the vertical. Find the horizontal 

 force and the tension of the string. 



2. A weight suspended by a string is pushed sideways by a horizontal force. 

 Show that as it is pushed farther from its position of rest, in which the string 

 is vertical, the tension continually increases. 



3. A weight of 100 pounds is suspended by two strings which make angles 

 of 60 with the vertical. Find their tensions. 



4. A weight of 30 pounds is tied to two extensible strings of natural length 

 2 feet, modulus of elasticity 100 pounds, and the other ends of the strings are 

 tied to two points at a horizontal distance 4 feet apart. Find the position in 

 which the weight can rest in equilibrium. 



5. A weight W is suspended by three equal strings of length I from hooks 

 which are the vertices of a horizontal equilateral triangle of side a. Find the 

 tensions of the strings. 



