Three forces N, 14N and 16N acting on a particle keep it in equilibrium. Find the angle between the forces 10N and 16N.
Question 1 Report
Three forces N, 14N and 16N acting on a particle keep it in equilibrium. Find the angle between the forces 10N and 16N.
Answer Details
The three forces are \(10\,\text{N},\ 14\,\text{N}\) and \(16\,\text{N}\) in equilibrium, so the resultant of the \(10\,\text{N}\) and \(16\,\text{N}\) forces must be equal in magnitude to \(14\,\text{N}\) (and opposite to it).
Let \(\theta\) be the angle between the \(10\,\text{N}\) and \(16\,\text{N}\) forces. Using the resultant (parallelogram) formula:
\[R^2 = 10^2 + 16^2 + 2(10)(16)\cos\theta = 14^2\] \[100 + 256 + 320\cos\theta = 196\] \[320\cos\theta = 196 - 356 = -160 \;\Rightarrow\; \cos\theta = -\tfrac{1}{2}\] \[\theta = 120^{o}\]The angle between the \(10\,\text{N}\) and \(16\,\text{N}\) forces is \(120^{o}\).
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