Question on: JAMB Physics - 2020
Consider the three forces acting at O and in equilibrium as shown in the figure. Which of the following equations is/are CORRECT?
I. P\(_1\) sin \(\theta_1\) = p\(_1\) cos \(\theta_2\)
II. P\(_3\) = P\(_1\) cos \(\theta_4\) + P\(_2 cos_2\)
III. P\(_1 \sin \theta_1 = P_2 \sin \theta_2\)
I only
II only
III only
I, II and III only
Here's the breakdown to determine the correct equation(s):
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Understanding Equilibrium: For a system to be in equilibrium, the net force in any direction must be zero. This means the sum of forces in the x-direction equals zero, and the sum of forces in the y-direction equals zero.
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Analyzing the Equations:
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I. P₁ sin θ₁ = P₁ cos θ₂: This equation is incorrect because it equates a component of P₁ (y-component) to another component of P₁ (x-component) which is not a valid equilibrium condition.
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II. P₃ = P₁ cos θ₄ + P₂ cos θ₂: This equation is incorrect. It attempts to relate P₃ to the x-components of P₁ and P₂, which is not generally valid.
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III. P₁ sin θ₁ = P₂ sin θ₂: This equation is correct. For equilibrium, the upward forces must equal the downward forces in the y-direction. Assuming that P1 and P2 have x-components and y-components, this is a statement of equilibrium in the y-direction.
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Conclusion: Therefore, only equation III is correct.
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