HOOKE'S LAW

In the seventeenth century a relationship between the extension of a string and the tension at each end was discovered experimentally by Hooke.

The relationship, known as Hooke's Law, states that, up to a certain point,

the extension, .r, in a stretched elastic string is proportional to the tension, T, in the string

i.e. T varies with x.

 

The Elastic Limit

As the extending forces applied to the string are steadily increased, there time when a further increase suddenly produces an extension much greater Hooke's Law would suggest. The string has become overstretched and will n' return to its natural length when it is released; it has gone beyond its Blast limit. Subsequently its extension bears no relationship to the tension and, this level of study, is no longer of any interest to us; in this book we deal with strings that have not exceeded their elastic limit.

 

SPRINGS

Hooke's Law applies to springs in a similar way as to elastic strings but there one important difference - a spring can be compressed as well as stretched.

When stretched, i.e. when it is in tension, a spring behaves in exactly the same w, as a stretched elastic string, i.e. equal and opposite tensions act inwards at the ends.

When a spring is compressed, the reduction in its length is called the concpre.ssit and the forces in the spring are an outward push, called a thrust, at each end.

The spring is said to be in compression and it obeys Hooke's Law where T is the thrust and r is the compression.