6:30 PM webwork.math.nau.edu .11 AT&T; PATH INDEPENDENT PATH INDEPENDENT At leas
ID: 2891687 • Letter: 6
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6:30 PM webwork.math.nau.edu .11 AT&T; PATH INDEPENDENT PATH INDEPENDENT At least one of the answers above is NOT correct. (1 point) Determine whether each of the following vector fields appears to be path independent Click on a graph to enlarge it) Note: You can earn 50% partial credit for 3-5 correct Preview My Answers Submit Answers Your score was recorded. You have attempted this problem 11 times. You received a score of 50% for this attempt. Your overall recorded score is 50%. You have unlimited attempts remaining.Explanation / Answer
When we move an object from point a to b then work performed by conservative field or we can say independent field does not depend upon the path of the field. Path independent and conservative are just two same terms.
The line integral of a vector field can be viewed as the total work performed by the force field on an object moving along the path.
Imagine that you have two stairways in your house: a gently sloping front staircase, and a steep back staircase. Since the gravitational field is a conservative vector field, the work you must do against gravity is exactly the same if you take the front or the back staircase. As long as the box starts in the same position and ends in the same position, the total work is the same.
So in independent path integral only depend upon the beginning and ending of point and not on the path and integral along all the paths give the same value.
so, independent path for above diagram is diagram 2,3,,4,6.
Opposite to conservative non conservative or dependent path depends on the path and it has diffenrent values along different path.
dependent path in diagram is 1,5
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