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Work Done by a Variant Force

In this section, the study of the basic definition of work of a variant force will be considered. This section can be omitted by those not familiar with calculus.

The drawing on the left shows a force being applied to an object along the path defined from the starting point to the ending point . In this case the force magnitude and direction can change along the path. In this general case, the work done by the force is defined by

 

In general, the element of path is which is extended in three dimensions to  . Depending on the functional dependence of the curve definition, the element of path can be rewritten as  .

The following exercises are direct applications of the previous definition.

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Work done by a Variant Force along the Curve of a Parabola.

 

  1) Question

 

a)

 

N

b)

119.5 J

 

c)

 

 

d)

 

 

e)

None of the above.

 

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Work done by a Variant Force along a Straight Line.

 

  2) Question

N

a)

120 J

 

b)

119.5 J

 

c)

 

 

d)

 

 

e)

None of the above.

 

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by Luis F. Sez, Ph. D.    Comments and Suggestions: LSaez@dallaswinwin.com