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Question

Calculate the work done if a particle is moved along a path AB−BC−CD−DE−EF−FA, as shown in the figure in presence of a force F=αyi^+2αxj^N , where x and y are in meters and α=-1Nm-1.


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Solution

Step 1. Given data

Force, F=αyi^+2αxj^N

α=-1Nm-1

Step 2. Calculating the work done from A to B, WAB

By using the formula of work, W

W=F.dr

WAB=αy.dx

WAB=α×101dx

WAB=-1 [eq1]

Step 2. Calculating the work done from B to C, WBC

WBC=2α×110.5dy

WBC=1 [eq2]

Step 3. Calculating the work done from C to D, WCD

WCD=α×110.5dx

WCD=14 [eq3]

Step 3. Calculating the work done from D to E, WDE

WDE=2α0.50xdy

WDE=12 [eq4]

Step 4. Calculating the work done from E to F and F to A

Work done from E to F and F to A is zero as x=0andy=0.

Step 4. Calculating the total work done, W

Adding all the equations, we get

W=0.75J

Therefore, the work done, W=0.75J


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