A constant force is rare. It is the variable force, which is more commonly encountered. Fig. a below is a plot of a varying force in one dimension. If the displacement Δx is small, we can take the force F (x) as approximately constant and the work done is then ΔW =F (x) Δx .
If the displacements are allowed to approach zero, then the number of terms in the sum increases without limit, but the sum approaches a definite value equal to the area under the curve in Fig. b Then the work done can be determined as shown below.
where ‘lim’ stands for the limit of the sum when Δx tends to zero. Thus, for a varying force the work done can be expressed as a definite integral of force over displacement .
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If the displacements are allowed to approach zero, then the number of terms in the sum increases without limit, but the sum approaches a definite value equal to the area under the curve in Fig. b Then the work done can be determined as shown below.
where ‘lim’ stands for the limit of the sum when Δx tends to zero. Thus, for a varying force the work done can be expressed as a definite integral of force over displacement .
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Friction introduction
Rolling Friction
Newton's First law of motion
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