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Four forces of magnitude P,2P,3P and 4P act aling the four sides of square ABCD in cyclic order. Use the vector method to find the resultant force?

Four forces of magnitude P,2P,3P and 4P act aling the four sides of square ABCD in cyclic order. Use the vector method to find the resultant force?

Grade:11

2 Answers

Rahul Parkar
8 Points
13 years ago

side 1 parallel side 3

considering this as X-axis,

P-3P=-2P i          (→ +ive)

for Y-axis

2P-4P=-2P j        (↑ +ive)

mod(∑F)=√(Fx2+Fy2)

            =√(4P2+4P2)

            =2P√2

 

Kushagra Madhukar
askIITians Faculty 628 Points
2 years ago
Dear student,
Please find the solution to your problem.
 
We have,
FAB = P i
FBC = 2P j
FCD = 3P ( – i)
FDA = 4P ( – j)
Hence, resultant vector,
Fr = FAB + FBC + FCD + FDA
    = (P i – 3P i) + (2P j – 4P j)
    = – 2P i – 2P j
Hence, |Fr| = [(-2P)2 + (-2P)2]1/2
Hence, |Fr| = 2√2 P
 
Thanks and regards,
Kushagra

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