1.

Draw force-displacement graph for a spring and find an expression for the potential energy of an elastic spring.

Answer»

Solution :(i) According to Hooke's law the restoring spring FORCE and displacement are linearly related as F =- kx, and are opposite in direction, the GRAPH between F and x is a straight line with dwelling only in the second and fourth quadrant as SHOWNIN Figure. (ii) The elastic potential energy can be easily CALCULATED by drawing a F-x graph. The shaded area (triangle) is the work done by the spring force. (iii) Area (base) (height) `= 1/2 xx (x) xx (kx)` .
`= 1/2 kx^2`

(iv) Work done is stored as the potential energy of the spring.
` therefore U = 1/2 kx^2`


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