Physics

Problem

0.50\,\text{kg}

block is attached to one end of a light spring of force constant

200\,\text{N}\,\text{m}^{-1}

placed on a rough horizontal table. The block is initially at the spring’s natural length. A constant horizontal force of

25\,\text{N}

pulls the block, stretching the spring by

0.20\,\text{m}

in the process. The coefficient of kinetic friction between block and table is

0.10

and

g=10\,\text{m}\,\text{s}^{-2}

. (i) Derive the expression for the work done by the spring force when it is stretched from its natural length to an extension

x

. (ii) For

x=0.20\,\text{m}

, calculate the work done by (a) the applied horizontal force, (b) the spring force, and (c) the frictional force. (iii) Hence determine the net work done on the block and the corresponding change in its kinetic energy. (iv) If the same experiment were performed on a perfectly smooth table, how would your answers to parts (ii) and (iii) change? Give numerical values where possible.

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