Question

four forces of magnitude p,2p,3p,4p act along the four sides of a square abcd in cyclic order.use the vector kethod to find the resultant force

Answer 1

the resultant of  forces along  AB and CD :  p - 3p =  - 2p  = P
     this is along  CD direction

resultant of forces along  BC and DA :  2p - 4p  = - 2p  = Q
  this is along DA direction.

since P and Q are equal in magnitude and are perpendicular to each other , it is easy to find the resultant.

The resultant of  forces P and Q will be    √2 2 p 
       the direction is  45 deg. to either  DA or BA.

Answer 2

Please check attachment for detailed solution.


We have used the triangle law of vector addition in 2nd method.


It also gave the same magnitude as 2√2p and direction as 45° from AB or DA. (or 225° we can say from initial vector AB .)

Hope it helped.

Thanks