A position dependent force F=7−2x+3x2 newton (where x is in meter) on a small body of mass 2 Kg & displace it from x=0 to x=5 m. Calculate the work done.
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Solution
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Step 1: Work done
Work done for small displacement can be defined as:
dW=Fdx....(1)
Step 2: Integrate the equation
Total work done can be calculated by integrating the equation (1) with limits x=0 to x=5m
∫dW=0∫5Fdx
∫dW=0∫5(7−2x+3x2)dx
⇒W=[7x−22x2+33x3]05
⇒W=35−25+125=135J
Hence, the work done is 135J
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