Mechanics: Mechanical Energy

 Mechanics: Mechanical Energy

As we all know from our earlier lessons that physics is the study of matter in relation to energy. Under mechanics, we will be dealing with the study of mechanical.

Under other branches like thermal physics, we will be studying thermal energy and the same goes for other branches whereby we will be dealing with concept of  electrical energy, light energy, energy possessed by electromagnetic waves, nuclear energy etc.

We will study mechanical energy under three heading;

■Relationship between work, mechanical energy and mechanical power.
■Potential energy stored in elastic materials.
■Minimization of mechanical energy for doing useful work.


Relationship between work, mechanical energy and mechanical power.

Work: Work is said to be done when a force moves a body through a particular distance in the direction of the force. When work is done, energy is expended. So, no work can be done without energy.

For example, considering the diagram below,

The work done in compressing a gas though a depth H,

Energy: Energy is expended whenever work is done, thus we can define energy as the capability of matter to do work due to their mass/weight, electrical charge etc.  

POWER is the rate at which energy is expended or total work done per unit time.                                                                           Power = 

We We have different forms of energy and energy resources. 

FORMS OF ENERGY

Mechanical energy

Thermal energy

Light energy

Sound energy

Electrical energy

Chemical energy

Solar energy

Nuclear energy  

   

Energy Resources 

The energy resources are generally of two kinds; the renewable and the non-renewable resources.                                                                                                                                                                                                             ■Renewable resources are those that can be re-used. E.g.,

●Solar energy used in solar cells                                                                                                       ●Wind energy used in turning windmills                                                                                         ●Hydro-electricity for generation of electricity in dams.

■Non-renewable resources are those that cannot be re-used. E.g., Petroleum, coal.                                                                                                                                         

Mechanical energy: Mechanical energy can either be a potential energy or kinetic energy.

The law of conservation of mechanical energy emphasizes the fact that the total mechanical energy of a system is the sum of its potential and kinetic energy.

The last equation gives the relationship between the maximum velocity and maximum height of falling bodies.
Since the velocity varies with the height of the body above the ground, and they are inversely related, we can generalize this equation as follows from the figure below.                                  

The velocity at point h above the ground will be,

Energy stored in elastic materials: The concept of elasticity

Elasticity is the ability of elastic materials to regain their normal form after deformation.
The deformation could either be caused by a tensile stress, shear stress or bulk stress.

Hooke’s Law (1), the applied force will always be directly proportional to the extension of an elastic material if the elastic limit is not exceeded.

....
Minimization of mechanical energy for doing useful work: The concept of machines.

The fact that we can’t survive without working is obvious, and no useful work can be done without energy, and we need enough energy to do great work. The work that has to be done requires more energy than usually available. How do we manage this?
  
This can be solved if we devise a means whereby relatively small energy (effort) can be use to do more work. The devices or equipments which allow little effort to do useful work are called MACHINES.

MACHINE is a device or equipment that makes our work easier or a device that allow little force called EFFORT to overcome a large force called LOAD.

The effort is the force applied to the machine and the load is the force overcome by the machine.                                                          
The ratio of the load to effort is called the MECHANICAL ADVANTAGE (M.A), and the more the mechanical advantage of the machine, the more efficient it will be.

The efficiency of a machine is the measure of the difference between the work done by the machine (work output) and the work done on the machine (work input).

 If the difference between the work output and the work input is very small, the machine is very efficient and if the difference is much, we say, the machine is not efficient or the machine has low efficiency.



Efficiency of a machine

Efficiency E of a machine is the ratio of the work output by the machine to the work input on the machine.

I.e. %E =  x 100%


The losses are usually due to the frictional force overcome by the machine and the one that exists between their moving parts.
The most efficient machine as of today is the electrical transformer as they have no moving part, they only work based on the principle of electromagnetic induction.

 But yet, it is not 100% efficient. Therefore, in practical, ideal machines does not exists.

Work output = Load (L) x Distance (DL) moved by load                                                                                                                                 Work input = Effort (E) x Distance (DE) moved by effort