Question

10. A particle starts from rest from origin and moves
along a parabolic path whose equation is y = x²
in the presence of a number of forces. One of
the forces acting on the particle is
F = (xi - 4zk)N . Find work done by this force F
when the particle moves from origin to x = 2m.
(2) 2 J
(1) Zero
(3) 1 J
(4) None​

Answer 1

Solution:

• Here they gave that, a parabolic path, $F=(Xi-4zk)N$ ,  

        $x_{i} =0(rest)-x_{f} =2$

• By using the basic formula,

                             $W=\int\limits^a _b {f} \, dx$    

• where,

            $a=$ the final distance

                $=2m$

          $b= initial(rest)$

             $=0$

• sub all the values in the formula

           $W=\int\limits^2 _0 {x} \, dx$

                $=\int\limits^2_0 [\frac{x^{2} }{2} ]$    

                $=\int\limits^2_0 [\frac{x_{f} }{2} -\frac{x_{i} }{2} ]$

                $=[\frac{2^{2} }{2} -\frac{o^{2} }{2} ]$

                $=[\frac{4}{2} -0]$

                $=2j$

Therefore the answer is 2joules.

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