Work Due To Raise Or To Accelerate A Body

·         When a body is raised in a gravitational field, its potential energy increased.

·         When a body is accelerated, its kinetic energy increases.

·         The conservation of energy principle requires that an equivalent amount of energy must be transferred to the body being raised or accelerated. Remember that energy can be transferred to a given mass by heat and work.If the energy transferred in the case obviously is not heat and it is not driven by a temperature difference, it must be work.

·         We conclude that:

1. The work needed to transfer a body is equal to the change in the potential energy of the body
2. The work transfer needed to accelerate a body is equal to the change in the kinetic energy of a body

Similarly, the potential or kinetic energy of a body represents the work that can be obtained from the body as it is lowered to the reference level or decelerated to zero velocity.

Work Associated With Stretching of Liquid Film

Consider liquid film attach to a wire frame. We kno that it will take sum force to strech the film by the moveable portion of the wire frame.

(I kno this isnt a wire frame, but u get the picture)

• The force has to overcome the microscopic forces on perpendicular to any line in the surface and the forces generated by these forces per unit length is called the surface tension σ(^N/_M­).

The work associated with the stretching of a film is also called suface tension work. It is determined from   W_Surface = ∫₁²σ•dA (kJ)                (2-31)                                           
Where dA = 2b•dx is the change in the surface area of the film. The factor 2 is due to the two film surfaces that are in contact with air. The force acting on the movable wire as a result of surface tension effects is F=2b•σ_s .Where σ is the surface tension force per unit length

Work Done on Elastic Bars

Solids are often modeled as linear springs because under the action of a force they contract or elongate and when the force is lifted, the return to their original lengths, like s spring.

· As long as the force is in the elastic range, that is not large enough to cause permanent deformation. (plastic)

· Therefore, the equations used for elastic solid bars.

Alternately, we can determine the work associated with the expansion or contraction of an elastic solid bar by replacing pressure P by its counterparts in solids, normal stress σ_n= F/A in the work expression:

W_elastic=∫₁²F•dx = ∫₁²σ_n®·•A•dx (kJ) (2-30)

Spring Work

Spring Work occurs when force is applied to a spring and the length of the spring changes.

 

·         When the length of the spring changes by a differential amount dx under the influence of a force F, the work done. That work is calculated as,  δWspring = F*dx                                (2-27)

·         To determine the total spring work, we need to know a functional relationship between F and X. 

·         For linear elastic springs, the displacement x is proportional to the force applied. That is  f=kx  (kN)                                                                                                                                    (2-28)

o   Where K is the spring Constant and has the unit (kN/m). The displacement x is measured from the undisturbed position of the spring (that is, x = 0 whenever F = 0). Substituting Eq. 2-28 into Eq. 2-27 and integrating yields

Wspring= 1/2 k{(x^2final)-(x^2initial)} (kJ) (2-29)

xinitial and xfinal are the initial and final displacements of the spring respectively, measured from the undisturbed position of the spring.

 Example: The force F required to compresss a spring x is given by F-F0 = kx Where k is the spring constant and F0 is the preload.Determine the work required to compress a spring whose spring constant is k=200 lbf/in in a distance of one inch starting from its free length where F0 =0 lbf. Express your answer in both lbf*ft and Btu.

=8.333 lbf*ft

=.0107 Btu

 

Mechanical Forms of Work

In elementary mechanics, the work done by a constant force F on a body a displaced s in the direction of the force given by w=Fs (kJ) (2-21)

If the force F is not constant, the work done is obtained by adding(i.e., integrating) the differential accounts of work, w=2/1 ∫ (F*ds)(kJ) (2-22)

Signs can be easily determined from the physical conditions:

1.       The work done on a system by an external force acting in the direction of motion is negative.

2.       Movement done on a system against an external force acting in the opposite direction to motion is positive.

The two requirements for a work interaction between a work system and its surroundings to exist:

1.       There must be a force acting on the boundary.

2.       The boundary must move.

No-Nos:

1.       The presence of forces on the boundary without any displacement on the boundary doesn’t constitute as work interaction.

2.       The displacement of the boundary without any force to oppose on drive this motion is not work interaction, since no energy is transferred

Mechanical Work is associated with the movement of the boundaries of a system or with the movement of the entire system as a whole

A few common forms of Mechanical Work Are:

Shaft Work

Spring Work

Work done on Elastic Bars