Spring

Definition

A spring is an elastic object that can store mechanical energy when compressed or stretched, and then release that energy to perform work. Springs are fundamental components in many mechanical systems, playing a crucial role in the conservation and transformation of energy.

5 Must Know Facts For Your Next Test

1. The potential energy stored in a spring is proportional to the square of the displacement of the spring from its equilibrium position.
2. The energy stored in a spring is equal to the work done in compressing or stretching the spring, which is given by the area under the force-displacement curve.
3. Springs can be used to store energy and release it later, making them useful in applications such as shock absorbers, clocks, and various mechanical devices.
4. The stiffness of a spring, known as its spring constant, determines how much force is required to stretch or compress the spring by a given distance.
5. The frequency of oscillation of a mass-spring system is determined by the spring constant and the mass of the object attached to the spring.

Review Questions

• Explain how the potential energy stored in a spring is related to its displacement from the equilibrium position.
  • The potential energy stored in a spring is proportional to the square of the displacement of the spring from its equilibrium position. This relationship is described by Hooke's Law, which states that the force required to stretch or compress a spring is proportional to the distance of the stretch or compression. The potential energy stored in the spring is equal to the work done in compressing or stretching the spring, which is given by the area under the force-displacement curve. As the spring is displaced further from its equilibrium position, the potential energy stored in the spring increases quadratically.
• Describe how the energy stored in a spring is transformed into kinetic energy when the spring is released.
  • When a spring is compressed or stretched and then released, the stored potential energy in the spring is converted into kinetic energy. As the spring returns to its equilibrium position, the potential energy is transformed into the kinetic energy of the object attached to the spring. This energy transformation is governed by the principle of conservation of energy, where the total mechanical energy (the sum of potential and kinetic energy) remains constant. The kinetic energy gained by the object as it moves away from the equilibrium position is equal to the potential energy that was initially stored in the compressed or stretched spring.
• Analyze the factors that determine the frequency of oscillation in a mass-spring system and explain how this relates to the conservation of energy.
  • The frequency of oscillation in a mass-spring system is determined by the spring constant and the mass of the object attached to the spring. Specifically, the frequency is inversely proportional to the square root of the mass-to-spring constant ratio. This relationship is derived from the principles of conservation of energy and Newton's laws of motion. As the object attached to the spring oscillates, its energy is continuously transformed between potential energy (stored in the spring) and kinetic energy (of the moving object). The frequency of this energy transformation is determined by the stiffness of the spring and the inertia of the attached mass. The conservation of energy ensures that the total mechanical energy of the system remains constant, with the energy simply oscillating between potential and kinetic forms at the characteristic frequency of the mass-spring system.

Related terms

Hooke's Law: Hooke's Law describes the linear relationship between the force applied to a spring and the resulting displacement, stating that the force required to stretch or compress a spring is proportional to the distance of the stretch or compression.

Potential Energy: Potential energy is the energy stored in an object due to its position or state, such as the energy stored in a compressed or stretched spring, which can be released to do work.

Kinetic Energy: Kinetic energy is the energy of motion, and when a spring is released, the stored potential energy is converted into kinetic energy, allowing the spring to perform work.