Question

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​

Answer 1

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.

Answer 2

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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