Discussion
The acceleration of the piston in a reciprocating steam engine is given by :
Answer: C
The piston acceleration is \(\omega^{2}r\left(\cos\theta + \frac{\cos 2\theta}{n}\right)\), where \(n = l/r\).
For a crank of radius r turning at \(\omega\) with connecting rod length l, the piston displacement is approximately \(x = r\left[(1 - \cos\theta) + \frac{\sin^2\theta}{2n}\right]\). Differentiating once gives the velocity and twice gives the acceleration:
\[ \begin{aligned} v &= \omega r\left(\sin\theta + \frac{\sin 2\theta}{2n}\right) \\ a &= \omega^2 r\left(\cos\theta + \frac{\cos 2\theta}{n}\right) \end{aligned} \]
The sine forms belong to the velocity expression, not the acceleration, and the minus signs are wrong: at \(\theta = 0\) the acceleration is greatest, \(\omega^2 r(1 + 1/n)\), which needs a plus.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development