Given v=3i+4j and force vector F=9i+12j, find:?

Question

Given v=3i+4j and force vector F, find:

(a) The component of F parallel to v

(b) The component of F perpendicular to v

(c) The work, W, done by force F through displacement v

Answer 1

(a)

Displacement vector V=3i+4j  .

Force vector F=9i+12j .

So the component of F parallel to V is  .

v=3i+4j   and F=9i+12j

F.V = 3*9 +4*12

F.V = 27+48

F.V = 75

So the component of vector F parallel to V is  .

So the  component of F parallel to V is  3i + (4/3) j .

Answer 2

(b)

Displacement vector V=3i+4j  .

Force vector F=9i+12j .

The component of F perpendicular to V is F - ( component of F parallel to v ) .

So now find for component of F parallel to v  :

The component of F parallel to V is  .

v=3i+4j   and F=9i+12j

F.V = 3*9 +4*12

F.V = 27+48

F.V = 75

So the component of vector F parallel to V is  .

So the  component of F parallel to V is  3i + (4/3) j .

 

The component of F perpendicular to V is F - ( component of F parallel to v ) .

F - ( component of F parallel to v ) = 9i+12j - (3i + (4/3) j )

                                                     =  9i+12j - 3i - (4/3) j 

                                                     = 6i +(32/3)j 

So the component of F perpendicular to V is 6i +(32/3)j .

 

Answer 3

(c)

The work W, done by a force F acting on an object through a displacement v is given by  W = F·d .

 W = F·d 

 W = (9i +12j ) · (3i +4j) 

 W = 9*3 + 12*4

 W = 27 + 48

W = 75 

So the work done by the force is 75 J .