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Obtain graphically and mathematically work done by a variable force. |
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Answer» Solution :(i) When the component of a VARIABLE force F acts on a body, the small work done (dW) by the force in producing a small displacement dr is given by the relation `dw = (f cos theta) dr` [F cos `theta` is the component of the variable force F] where, F and `theta` are variables. (II)The TOTAL work done for a displacement from initial position `r_(i)` to FINAL position `r_(f)` is given by the relation, `W = int_(r_(i))^(r_(f))dW = int_(r_(i))^(r_(f))F cos theta dr ""`.....(1) (iii) A graphical representation of the work done by a variable force is shown in Figure 1. The area under the graph is the work done by the variable force. 
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