# Conservative Forces

JoVE Core
Mechanical Engineering
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JoVE Core Mechanical Engineering
Conservative Forces

### Nächstes Video11.8: Potential Energy

A force is known as conservative, if its work depends only on the initial and final positions, regardless of the path followed.

Two examples of conservative forces are the weight of a body and the spring force.

Weight is the force experienced by an object due to gravity.

If the block hanging from a crane is displaced against gravity by a vertical displacement of dr, then work done is the dot product of the force and the vertical displacement.

The work done is negative as the weight acts in the opposite direction of the displacement.

Since the work done is independent of the path taken and only depends on the vertical displacement, the weight is a conservative force.

Similarly, for linearly elastic springs, when a block is displaced horizontally, the work depends only on the spring's initial and final positions, and is independent of the path taken. So, the forces exerted by springs are also conservative.

## Conservative Forces

Conservative forces are an essential concept in the field of mechanical engineering. Understanding the properties and characteristics of these forces is crucial to the design and analysis of mechanical systems.

Conservative forces are forces that are dependent only on the initial and final positions of an object and that are independent of the path that the object takes between these positions. These forces conserve energy, which means that the work done by the force is independent of the path taken. Examples of conservative forces include gravity, electrostatic forces, and springs modeled by Hooke's Law.

Consider a ball rolling down a hill. The work done by gravity on the ball as it moves from the top of the hill to the bottom is the same, regardless of the path the ball takes down the hill. Conservative forces are also useful in the design of mechanical systems. Engineers can use these forces to calculate the amount of work done by a force on a system and determine the energy required to move an object from one position to another. This information can then be used to design more efficient systems and to minimize energy loss due to non-conservative forces such as friction.

Another critical aspect of conservative forces is that they can be represented by a potential energy function, which is defined by the relationship between the force and the position of the object. This function describes the energy stored in a system due to the position of an object.