The work required to stretch a certain spring from an elongation of4.44 cm to an

Question

The work required to stretch a certain spring from an elongation of4.44 cm to an elongation of 5.44 cm is 31.9 J. (a) Is the work required to increase theelongation of the spring from 3.44 cm to4.44 cm greater than, less than, or equalto 31.9 J?
1---Select---less thangreater thanequal to
(b) Verify your answer to part (a) by calculating the requiredwork.
2 J (a) Is the work required to increase theelongation of the spring from 3.44 cm to4.44 cm greater than, less than, or equalto 31.9 J?
1---Select---less thangreater thanequal to
(b) Verify your answer to part (a) by calculating the requiredwork.
2 J

Explanation / Answer

(a). answer is less than (b). work done to streach the spring from the elongationfrom x to x ' is W = ( 1/ 2) k [ x '2 - x 2 ] In first case   x = 4.44 cm                    x ' = 5.44 cm So,   W = 4.94 k given W = 31.9 J S, spring constant k = 31.9 / 4.94                                = 6.457 units In second case x = 3.44 cm                        x ' = 4.44 cm So, work done W ' =  ( 1/ 2) k [ x '2 - x 2 ]                               =  ( 1/ 2) k [ 4.44 2 - 3.442 ]                               = 3.94 k                               = 3.94 * 6.457 J                               = 25.44 J

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