Vertical elastic strings and springs

Understanding the Basics of Vertical Elastic Strings and Springs

  • An elastic string is an idealised model where the string is massless, non-rigid, and can be stretched without limit.
  • A spring is another form of elastic object, which can either stretch (elongate) or compress depending on the forces applied. Hooke’s Law usually describes its behaviour.
  • The extension of a spring is the amount by which it has lengthened due to a stretching force.
  • The natural length of an elastic string or spring is its length when it is not under tension or compression.

Hooke’s Law

  • Hooke’s Law states that the force required to extend or compress a spring by some distance scales linearly with respect to that distance.
  • The law can be expressed by the formula F = kx where F is the force exerted by the spring, x is the displacement of the spring from its natural length, and k is a constant known as the spring constant.
  • The minus sign in the formula denotes that the force exerted by the spring is a restoring force, i.e., it acts in the opposite direction to the displacement.
  • The spring constant is different for different materials and different springs. It shows how resistant a spring is to being deformed.

Energy in Springs

  • The elastic potential energy stored in a stretched or compressed spring can be calculated using the formula E = 1/2 kx^2, where E is the energy, k is the spring constant, and x is the displacement of the spring from its natural length.
  • When a spring is stretched or compressed, it stores elastic potential energy, when this stretching or compressing force is released, the spring returns to its natural length and the stored energy is converted to kinetic energy.
  • As a spring oscillates (expands and compresses), energy is transferred back and forth between kinetic and potential energy, which explains the motion of a mass-spring system.

Practical Applications of Understanding Springs

  • Understanding spring and elastic string behaviour is important in various aspects of physics and engineering, such as designing suspension in vehicles, in mattress and furniture design, architecture, and even in sports equipment.
  • Understanding energy transfers in spring-mass systems can help us understand mechanical oscillations and vibrations, which have a huge range of applications, from musical instruments to seismic waves.