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What is potential energy. The potential energy U is defined as the energy stored in an object subjected to a conservative force. thermal engineering

## What is potential energy

**potential energy**, U, is defined as the**energy saved**in an object subjected to a conservative force. Common types include the**potential energy of gravity**, Die**elastic potential energy**an extended spring, and the**electrical potential energy**an electric charge in an electric field and so on.

Let's assume that**mechanical energy**(E_{mech}), this is the energy associated with that**Movement**And**Position**of an object usually in a force field (e.g. gravitational field).**M****mechanical energy**(and also thermal energy) can be divided into two categories, transient and stored. Transient energy is energy in motion, ie energy that is transferred from one place to another. Stored energy is the energy contained in a substance or object. Transient mechanical energy is commonly referred to as**work**. Stored mechanical energy exists in one of two forms:**kinetic**or**potential**:

**potential energy**. The potential energy U is defined as the energy stored in an object subjected to a conservative force. Common types include an object's gravitational potential energy, which depends on its mass and its distance from the center of mass of another object.**Kinetic energy**. the kinetic energy,*K*, is defined as the energy stored in an object due to its motion. It depends on the speed of an object and is the ability of a moving object to work on other objects when colliding with them.

## Examples of potential energy

**Gravitational Potential Energy:**

In classical mechanics, gravitational potential energy (U) is the energy possessed by an object due to its position in a gravitational field. The gravitational potential (V; the gravitational energy per unit mass) at a location is equal to the work (energy transferred) per unit mass that would be required to move the object from a fixed reference location to the object's location. The most common use of gravitational potential energy is for an object near the earth's surface, where the gravitational acceleration can be assumed to be constant at about 9.8 m/s^{2}.

**U = mgh**

**Elastic potential energy**:

Elastic potential energy is potential energy released as a result of the deformation of an elastic object, such as a B. the elongation of a spring is stored. It depends on the spring constant k and the stretched path.

**U = 1/2 kx ^{2}**

**Electrical potential energy**:

Electric potential energy is potential energy resulting from conservative Coulomb forces associated with the configuration of a specific set of point charges within a defined system. For example, if a positive charge Q is fixed at a certain point in space, any other positive charge brought close to it will experience a repulsive force and therefore have potential energy.

**U = kQq/R**

## conservation of mechanical energy

First the principle of**conservation of mechanical energy**was ascertained:

**The total mechanical energy**(defined as the sum of its potential and kinetic energies) of a particle on which only conservative forces act**is constant**.

See also:conservation of mechanical energy

**An isolated system**is one in which**no external force**causes energy changes. If only**conservative forces**act on an object and**U**is the**potential energy**function for the total conservative force, then

**E**_{mech}**= U + K**

**The potential energy U**, depends on the position of an object subjected to a conservative force.

It is defined as the object's ability to do work and is increased when the object is moved in the opposite direction of the direction of the force.

**The potential energy**assigned to a system consisting of the earth and a nearby particle**potential energy of gravity**.

**the kinetic energy, K**, depends on the speed of an object and is the ability of a moving object to work on other objects when colliding with them.

**K = ½ mv ^{2}**

The above definition (**E**_{mech}**= U + K**) assumes that the system is**free from friction**and other**non-conservative forces**. The difference between a conservative and non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path.

In every real situation**friction forces**and other non-conservative forces exist, but in many cases their impact on the system is so small that the principle of**conservation of mechanical energy**can be used as a good approximation. For example, the frictional force is a non-conservative force because it acts to reduce the mechanical energy in a system.

Note that non-conservative forces do not always reduce mechanical energy. A non-conservative force changes the mechanical energy, there are forces that increase the total mechanical energy, such as the force provided by a motor or motor is also a non-conservative force.

## Block sliding down a smooth incline

The 1 kg block starts at a height H (let's say 1 m) above the ground**potential energy** **mgH**And**kinetic energy**that equals 0. It slides to the ground (with no friction) and arrives with no potential energy and no kinetic energy**K = ½ mv ^{2}**. Calculate the speed of the block on the ground and its kinetic energy.

*E*

_{mech}

*= U + K = const**=> ½ Mw*^{2}*= mgH*

*=> v = √2gH = 4,43 m/s*

*=>K*_{2}*= ½ x 1 kg x (4,43 m/s)*^{2}*= 19,62 kg.m*^{2}*.S*^{-2}*= 19,62 J*

## Pendulum

Suppose a**Pendulum**(Ball of mass m suspended from a cord of length**L**that we pulled up so that the ball has height**H<L**above its lowest point on the arc of its stretched string motion. The pendulum is exposed to this**conservative Gravitational force**where frictional forces such as drag and friction at the pivot point are negligible.

We free it from the rest.**How fast does it go down?**

The pendulum is enough**greatest kinetic energy**And**lowest potential energy**if in**vertical position**, because at this point it will have the greatest speed and will be closest to the earth. On the other hand, it will have its**lowest kinetic energy**And**greatest potential energy**In the**extreme positions**of its momentum because it has no speed at those points and it is furthest from Earth.

When the amplitude is limited to small swings, the period is*T*of a simple pendulum, the time for a complete cycle is:

Wo** L**is the length of the pendulum and

**is the local acceleration due to gravity. For small swings, the swing duration is about the same for swings of different sizes. That is,**

*G***the period is independent of the amplitude**.

References:

**Reactor physics and thermal hydraulics:**

- J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2. Aufl., Addison-Wesley, Reading, MA (1983).
- J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3. Aufl., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
- W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0-471-39127-1.
- Glasstone, Sesonske. Nuclear reactor technology: Reactor system technology, Springer; 4th edition, 1994, ISBN:978-0412985317
- Todreas Neil E., Kazimi Mujid S. Core Systems Volume I: Thermal-Hydraulic Fundamentals, Second Edition. CRCPress; 2nd edition, 2012, ISBN:978-0415802871
- Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. jumper; 2015, ISBN:978-3-319-13419-2
- Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
- Small shaker C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
- U.S. Department of Energy, THERMODYNAMICS, WEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Band 1, 2 und 3. Juni 1992.

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