Determine the resultant r of the given forces.f1 acting with a magnitude of 12 N and f2 acting at an angle of 60° to f1 with a magnitude of 12 N. (Assume f1 acts in the positive x-direction.)
Question
Determine the resultant r of the given forces.f1 acting with a magnitude of 12 N and f2 acting at an angle of 60° to f1 with a magnitude of 12 N. (Assume f1 acts in the positive x-direction.)
Solution
To find the resultant of the two forces, we can break down the problem into two steps:
Step 1: Resolve the forces into their components. The force f1 is acting along the x-axis, so its components are: f1x = 12N (cos 0°) = 12N f1y = 12N (sin 0°) = 0
The force f2 is acting at an angle of 60° to f1, so its components are: f2x = 12N (cos 60°) = 6N f2y = 12N (sin 60°) = 10.4N
Step 2: Add the components to find the resultant force. The x-component of the resultant force (rx) is the sum of the x-components of f1 and f2: rx = f1x + f2x = 12N + 6N = 18N
The y-component of the resultant force (ry) is the sum of the y-components of f1 and f2: ry = f1y + f2y = 0 + 10.4N = 10.4N
Finally, we can find the magnitude of the resultant force using the Pythagorean theorem: r = sqrt(rx^2 + ry^2) = sqrt((18N)^2 + (10.4N)^2) = 20.8N
So, the resultant of the two forces is 20.8N.
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