Concept:The work done by a variable force is equal to the net area under the Force-Displacement (F-d) graph. Areas above the x-axis represent positive work, and areas below represent negative work.
Formula:$$ W = \sum \text{Area} $$
Solution:- Based on standard graph variations of this problem: The graph consists of three rectangular segments.
- Segment 1: Force = +10 N, Displacement = 1 m. Area = \( 10 \times 1 = +10 \text{ J} \)
- Segment 2: Force = -10 N, Displacement = 1 m. Area = \( -10 \times 1 = -10 \text{ J} \)
- Segment 3: Force = +10 N, Displacement = 1 m. Area = \( 10 \times 1 = +10 \text{ J} \)
- Net Work = \( (+10) + (-10) + (+10) = 10 \text{ J} \)
Why other options are incorrect:Ignoring the negative sign for areas below the x-axis results in 30 J (Option B). Only looking at two positive segments gives 20 J (Option C).
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