A force F=-2i + 3j + k unit has its point of application moved from A to B where AB = 3i + 4j - 4k. What is the work done by the force?

Given data:-

   F= -2i + 3j + k

   d = AB = 3i + 4j – 4k 

   w = ?

Solution:-

    Here we have to find the work done by the given force and as we have formula for work done

 w = f . dcos(Ѳ) , work done is cross product .As given we have force and displacement in vector form. We also know that for dot product :-

i . i cos(0) = i.i (1) = 1 ,            j . j = 1 ,                           k . k =1 ,

i . j cos(90) = 0 ,                  j . k = 0 ,                k . i = 0   { because cos(90) = 0 }

so we simply multiply  i.i , j.j , k.k

So   w = f . d cos(Ѳ) = (i)(i)cos(0) + (j)(j)cos(0) + (k)(k)cos(0)

        {Therefore  cos(0) = 1}

       w=  (-2)(3) + (3)(4) +  (1)(-4)          

       w = - 6 + 12 – 4

       w = -10 + 12

       w = 2 J .

SI unit of work is (joule) same as of energy. So we write joule with the  value of work.

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2 )   One another concept , work done is independent of path followed between two points in gravitational field , So gravitational field is a conservative field . Conservative forces are not dependent of path followed by object  , while non – conservative forces are dependent on path followed by object .

3 ) Air friction can …………………… the time period of simple pendulum .

A )  Increase ,                                              B )  Decrease  ,

C ) Not effected by air friction ,                  c ) None of these ,

Correct Answer : -       A )  Increase ,

4 )  Greater the least count in measured value , ……………… will be its accuracy .

A )  Greater ,                                     B )  Smaller ,

C ) Not effected ,                              c ) None of these ,

Correct Answer : -       A )  Greater  , 

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