Question

if a particle is acted upon by a force .f=xi+yj+zk N/m where x,y,z are in metres.find the work done by the force when the particle moves from (2,2,2) to (3,4,1).

Answer 1

Answer:

Work done is x +2y - z...

Answer 2

Given :

A particle is acted upon by a force of :

$F=xi+yj+zk\ N/m$

To find:

Work done by the force when the particle moves from (2,2,2) to (3,4,1).

Solution,

Work done is given by :

$W=\int\limits^3_2{x{\codt} dx}+\int\limits^4_2{y{\codt} dy}+\int\limits^1_2{z{\codt} dz}\\\\W=\dfrac{x^2}{2}|^3_2+\dfrac{y^2}{2}|^4_2+\dfrac{z^2}{2}|^1_2\\\\W=\dfrac{1}{2}(3^2-2^2)+\dfrac{1}{2}(4^2-2^2)+\dfrac{1}{2}(1^2-2^2)\\\\W=7\ J$

So, the work one by the particle is 7 Joules.

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Work done

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