hookes-law

Up to now, strings have been modelled as inextensible

• they cannot stretch (inelastic)

• we assume that the tension measured at any point along the string is the same constant value

Things that stretch (or compress, e.g. springs) are called elastic 

Imagine two elastic strings held taut and at rest, but with one stretched further than the other

• measuring the tension at different points along one string gives the same value,

• but that “value” will be higher for the more stretched string than for the less stretched string

Hooke’s law tells us that the value of tension, N, depends on how far it’s been stretched (the extension, metres) beyond its natural (unstretched) length ( metres)

• The law is 

• where  is the modulus of elasticity, with units of Newtons,

  • it measures the stiffness of the material the string (or spring) is made from,

  • the higher  is, the stiffer the string / spring is

Springs can be compressed but elastic strings can’t (they’d go slack)

• Hooke’s law works for compression of springs too

• Instead of measuring extension, measures the length of compression (from its natural length)

  • just make sure any tension arrows reverse direction to be compression (thrust) arrows!

Imagine a particle of mass kg attached to the end of a light elastic string of natural length  metres, with modulus of elasticity N

The other end of the string is attached to a ceiling at the point O and the particle hangs at rest at the point <