Hooke's law

Examples of Hooke's law in the following topics:

• Hooke's Law

  • Many weighing machines, such as scales, use Hooke's Law to measure the mass of an object.
  • In simple terms, Hooke's law says that stress is directly proportional to strain.
  • Mathematically, Hooke's law is stated as:
  • In such a case, Hooke's law can still be applied.
  • The red line in this graph illustrates how force, F, varies with position according to Hooke's law.

• Simple Harmonic Motion

  • ., it follows Hooke's Law) .
  • Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law.
  • For one-dimensional simple harmonic motion, the equation of motion (which is a second-order linear ordinary differential equation with constant coefficients) can be obtained by means of Newton's second law and Hooke's law.
  • Using Newton's Second Law, Hooke's Law, and some differential Calculus, we were able to derive the period and frequency of the mass oscillating on a spring that we encountered in the last section!
  • The net force on the object can be described by Hooke's law, and so the object undergoes simple harmonic motion.

• Springs

  • Spring force is conservative force, given by the Hooke's law : F = -kx, where k is spring constant, measured experimentally for a particular spring and x is the displacement .
  • Plot of applied force F vs. elongation X for a helical spring according to Hooke's law (solid line) and what the actual plot might look like (dashed line).

• Elasticity, Stress, and Strain

  • Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke's law is obeyed.
  • In equation form, Hooke's law is given by $F = k \Delta L$ , where $\Delta L$ is the change in length.

• Stress and Strain

  • Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke's law is obeyed.
  • In equation form, Hooke's law is given by $F = k \cdot \Delta L$ where $\Delta L$ is the change in length and $k$ is a constant which depends on the material properties of the object.

• Period of a Mass on a Spring

  • The name that was given to this relationship between force and displacement is Hooke's law:
  • A typical physics laboratory exercise is to measure restoring forces created by springs, determine if they follow Hooke's law, and calculate their force constants if they do .
  • A common example of an objecting oscillating back and forth according to a restoring force directly proportional to the displacement from equilibrium (i.e., following Hooke's Law) is the case of a mass on the end of an ideal spring, where "ideal" means that no messy real-world variables interfere with the imagined outcome.
  • The motion of a mass on a spring can be described as Simple Harmonic Motion (SHM), the name given to oscillatory motion for a system where the net force can be described by Hooke's law.
  • In contrast, increasing the force constant k will increase the restoring force according to Hooke's Law, in turn causing the acceleration at each displacement point to also increase.

• Elastic Potential Energy

  • A graph shows the applied force versus deformation x for a system that can be described by Hooke's law .
  • A graph of applied force versus distance for the deformation of a system that can be described by Hooke's law is displayed.

• Sinusoidal Nature of Simple Harmonic Motion

  • If a system follows Hooke's Law, the restoring force is proportional to the displacement.

• Fracture

  • The straight segment is the linear region where Hooke's law is obeyed.

• Forced motion

  • Figure 1.2: A linear spring satisfies Hooke's law: the force applied by the spring to a mass is proportional to the displacement of the mass from its equilibrium, with the proportionality being the spring constant.