Primary unbalanced force — the primary inertia force of a reciprocating mass attains its maximum value when the crank angle with the line of stroke is at which positions?
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A0° and 90°
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B0° and 180°
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C90° and 180°
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D180° and 360°
Answer
Correct Answer: 0° and 180°
Explanation
Introduction / Context: The primary unbalanced force in a reciprocating mechanism varies sinusoidally with crank angle. Recognizing where it peaks is important for balancing strategies and bearing load estimation.
Given Data / Assumptions:
- Primary force Fp=m r ω² cos θ (first harmonic).
- θ is the angle between crank and line of stroke.
- Constant speed ω.
Concept / Approach: The magnitude of Fp is maximum when |cos θ|=1 and minimum when cos θ=0. Therefore, maxima occur at θ=0° and 180° (along the line of stroke), not at quadrature.
Step-by-Step Solution:
1) Write Fp=m r ω² cos θ.2) Maximize |cos θ| → |cos θ|=1 at θ=0° and 180°.3) Conclude peak primary shake at inner/outer dead centers.Verification / Alternative check: A plot of Fp against θ shows peaks at 0° and 180° and zeros at 90° and 270°.
Why Other Options Are Wrong:0° and 90° — includes one maximum and one zero.90° and 180° — includes a zero and a maximum.180° and 360° — 360°≡0°, duplicates same position but omits the other distinct maximum at 180°.
Common Pitfalls: Mixing primary and secondary components; forgetting that the cosine term peaks on the line of stroke.
Final Answer: 0° and 180°.