forces and elasticity

• Change of shape

  When a force acts on an object, the object may change shape by bending, stretching or compressing.
• there must be more than one force acting to change the shape of a stationary object in the following ways:

  • Bend an object's ends past each other, eg when an archer pulls an arrow back against a bow.
  • Pull an object's ends apart, eg when a rubber band is stretched.
  • Push an object's ends together, eg when an empty drinks can is squashed.
• A change in shape is called deformation:

  • elastic deformation = reversed when the force is removed
  • inelastic deformation = not fully reversed when the force is removed - there is a permanent change in shape

  A rubber band undergoes elastic deformation when stretched a little.

  A metal drinks undergoes inelastic deformation when it is squashed.
• Hooke's law

  The extension of an elastic object (such as a spring) is directly

  proportional to the force applied, provided that the limit of

  proportionality is not exceeded.
• force = spring constant × extension

  F = k e

  force, F, in newtons, N

  spring constant, k, in newtons per metre, N/m

  extension, e, in metres, m
• Work is done when...

  a spring is extended or compressed. 

  • Elastic potential energy is stored in the spring. Provided inelastic deformation has not happened
  • the work done is equal to the elastic potential energy stored.
• Linear extension and non-linear extension

  • Non-linear extension and inelastic deformation can be seen above the limit of proportionality. The limit of proportionality is also described as the 'elastic limit'.
  • Linear extension and elastic deformation can be seen below the limit of proportionality
  • The gradient of a force-extension graph before the limit of proportionality is equal to the spring constant.
• calculate work done in stretching (or compressing) a spring

  (up to the limit of proportionality) using the equation:

  elastic potential energy = 0.5 × spring constant × extension 2

  Ee = 1/2 k e2
• required practical

  1. Clamp stand, two bosses and two clamps - place a heavy weight on clamp stand to stop it falling over
  2.  Attach a metre ruler and a spring (ruler at the 0 point) 

  • Metre ruler should be vertical or readings will be inaccurate 
  • End of spring has a point and this should be horizontal (gives us readings)

  1. Mean the pointers current positive (the unstretched length with no force attached) 
  2. Add a 1N weight and read position of pointer, repeat process taking down the readings 
  3. To work out the extension, subtract length of the unstretched length from the reading