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

0 votes
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
asked Nov 4, 2014 in PRECALCULUS by anonymous
reshown Nov 4, 2014 by bradely

3 Answers

0 votes

(a)

Displacement vector V=3i+4j  .

Force vector F=9i+12j .

So the component of F parallel to V is image .

v=3i+4j   and F=9i+12j

F.V = 3*9 +4*12

F.V = 27+48

F.V = 75

image

So the component of vector F parallel to V is  .

image

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

answered Nov 4, 2014 by friend Mentor
0 votes

(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 image .

v=3i+4j   and F=9i+12j

F.V = 3*9 +4*12

F.V = 27+48

F.V = 75

image

So the component of vector F parallel to V is  .

image

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 .
 
answered Nov 4, 2014 by friend Mentor
edited Nov 4, 2014 by friend
0 votes
(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·
 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 .

answered Nov 4, 2014 by friend Mentor

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