Examples of Mechanical Energy

What is Mechanical Energy

conservartion-of-mechanical-energy-pendulumIn physics, mechanical energy (Emech) is the energy associated with the motion and position of an object usually in some force field (e.g. gravitational field). Mechanical energy (and also the thermal energy) can be separated into two categories, transient and stored. Transient energy is energy in motion, that is, energy being transferred from one place to another. Stored energy is the energy contained within 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. Potential energy, U, is defined as the energy stored in an object subjected to a conservative force. Common types include the gravitational potential energy of an object that 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 because of its motion. It depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them.

Example: Block sliding down a frictionless incline slope

The 1 kg block starts out a height H (let say 1 m) above the ground, with potential energy mgH and kinetic energy that is equal to 0. It slides to the ground (without friction) and arrives with no potential energy and kinetic energy K = ½ mv2. Calculate the velocity of the block on the ground and its kinetic energy.

Emech = U + K = const

=> ½ mv2 = mgH

=> v = √2gH = 4.43 m/s

=> K2 = ½ x 1 kg x (4.43 m/s)2 = 19.62 kg.m2.s-2 = 19.62 J

Example: Pendulum

conservartion-of-mechanical-energy-pendulumAssume a pendulum (ball of mass m suspended on a string of length L that we have pulled up so that the ball is a height H < L above its lowest point on the arc of its stretched string motion. The pendulum is subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible.

We release it from rest. How fast is it going at the bottom?

conservartion-of-mechanical-energy-pendulum2

The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points.

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

period-of-pendulum-conservation-of-energy

where L is the length of the pendulum and g is the local acceleration of gravity. For small swings the period of swing is approximately the same for different size swings. That is, the period is independent of amplitude.

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See above:

Mechanical Energy