If two concurrent forces A and B acting on a point are
200 N and 300 N. What is the magnitude of the
resultant force, if it makes an angle of 50° with each
force?
A. 471.08 N
B. 455.12 N
C. 400.56 N
Answers
Given,
Two concurrent forces 200 N and 300 N make an angle of 50° with each other.
To Find,
The net resultant force
Solution,
The formula for calculating the resultant force is
F net = √(A²+B²+2AB cos∅), where ∅ is the angle between the two vectors.
= √(200²+300²+2(200)(300) cos 50) { The value of cos 50 = 0.62}
= √(130000+76800)
= 471.08 N
Hence, the correct answer is option (a) 471.08 N.
The magnitude of resultant force is B. 455.12 N.
Given - Force A, Force B and angle 50°
Find - Magnitude of resultant force
Solution - The force will be calculated by the formula -
Force = ✓(A² + B² + 2AB cos theta)
Keep the values in formula
Force = ✓(200² + 300² + 2*200*300*cos 50°)
Taking square
Force = ✓(40,000 + 90,000 + 1,20,000*0.6)
Performing addition and finding cos 50°
Force = ✓(1,30,000 + 77,134.5)
Performing addition
Force = ✓2,07,134.5
Taking square root
Force = 455.12 N
Hence, the resultant force is B. 455.12 N.
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