The forces whose magnitude is in the ratio of 3:5 give a resultant of 35N. If the angle b/w them is 60°. Find the magnitude of each force.
Question
The forces whose magnitude is in the ratio of 3:5 give a resultant of 35N. If the angle b/w them is 60°. Find the magnitude of each force.
Solution
Sure, let's solve this step by step.
Step 1: Let's denote the forces as F1 and F2. Given that the ratio of their magnitudes is 3:5, we can say F1 = 3x and F2 = 5x.
Step 2: The resultant force (R) is given by the formula:
R = sqrt[(F1)^2 + (F2)^2 + 2F1F2*cosθ]
where θ is the angle between the forces.
Step 3: Substituting the given values into the formula, we get:
35 = sqrt[(3x)^2 + (5x)^2 + 23x5x*cos60]
Step 4: Simplifying the equation, we get:
35 = sqrt[9x^2 + 25x^2 + 30x^2]
35 = sqrt[64x^2]
Step 5: Solving for x, we get:
x = 35 / sqrt[64] x = 35 / 8 x = 4.375 N
Step 6: Now, we can find the magnitudes of the forces F1 and F2:
F1 = 3x = 34.375 = 13.125 N F2 = 5x = 54.375 = 21.875 N
So, the magnitudes of the forces are 13.125 N and 21.875 N.
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