Take the integral w 12 f ds along the path s force f

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take the integral W 12 = F ds along the path S. Force F is assumed to be known at each point along the path; the component of the force along the direction of path element ds is obtained and then the product of force component and path element evaluated. The sum of these along the path is considered the evaluation of the integral along the path from point 1 to point 2. This is known as the line integral (since its evaluated along a line). In order to do this experiment we need a rod mounted vertically on a table, spring balance, additional spring and pointer, a protractor, metal stick, wax block, kg weights, masking tape, and copier paper. To set up your workspace you fasten a piece of paper securely to the laboratory table near a vertical rod. To do the first line integral of this experiment with a protractor sketch a suitable semicircular path on paper. Next slip the loop of the balance over the vertical rod attached to the table, attach the auxiliary spring and pointer to the balance and check if the pointer will trace the curve you drew on the paper. Pretend that the balance still gives the tension in the system. Next divide the semi-circle into suitable segments, which can be approximated by straight lines. At each end of the segments of the semi-circle, place the pointer and note down near each point the reading of the balance. Next without removing the paper, unscrew the vertical rod from its place and with a ruler sketch a line from each point on the paper to the center of the hole where the rod was located. Use a protractor to obtain the angle between line segments. Next in order to the second line integral part for the experiment, locate the square in your laboratory on the floor. Using a spring balance, drag the wax block around the square, taking the reading of the balance at closely-spaced points all the way around the square.
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