if the force acting on a particle at any point (x'y'z) is (5xi+xyj+zk) how much work is done when the particle moves from the point (5,2,1)to the point (5,3,2)
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Given,
The force (F) acting on a particle at any point (x,y,z) = (5xi+xyj+zk)
Initial point = (5,2,1)
Final point = (5,3,2)
To Find,
Work done when the particle moves from (5,2,1) to (5,3,2)
Solution
Initial position vector (ri) = 5i+2j+1k
Final position vector (rf) = 5i+3j+2k
thus, displacement vector (d) = rf-ri
= (5i+3j+2k) - (5i+2j+1k)
= 1j+1k
We know that,
Work Done (W) = F.d
thus, W = (5xi+xyj+zk).(1j+1k)
= xy+z
Since it is a definite integration, let's put the initial and final values of x, y, and z
W = (5x3+2) - (5x2+1)
= 17-11
= 6
Hence, the work done is 6 units.
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