Pl. explain the graph of spring having potential energy and kinetic energy w.r.t. total energy. Why graphs are inverted parabolas for U and KE

Asked by VENIKA SINGHAL | 2nd Sep, 2011, 11:52: AM

Expert Answer:

Consider a massless spring of natural length 'l', one end of which is fastened to a wall. The other end is attached to a block, which is slowly pulled on a smooth horizontal surface, to extend the spring. If we take the spring as a system, when it is elongated by a distance 'x', the tension in it is kx, where 'k' is the spring constant. The force exerted on the spring are

1) kx towards left by the wall.

2) kx towards right by the block.

Let us calculate the work done on the spring.

 

 

The force by the wall does no work, since the point of application is fixed.

The work is positive as the force is towards right and the particles of the spring, also move towards right when the spring is elongated by an amount 'x', from its natural length. The same is applicable to compression.

The variation of potential energy with distance 'x' is shown in the graph.

The same formula for potential energy of the spring can also be obtained graphically, by plotting the variation of restoring force (F) with displacement (x), within elastic limits.

Taking the potential energy of the spring in the unstretched position as zero, the potential energy of the spring having displacement x, is equal to the area of the triangle, 

The constant interchange of energy between potential and kinetic forms is essential for producing and maintaining any type of oscillation.
 

 

The figure shows graphs of kinetic energy and potential energy versus displacement. Each of them is a parabola. The sum of the potential energy and the kinetic energy values remains constant as represented by the horizontal line.

Answered by  | 2nd Sep, 2011, 01:20: PM

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