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Q69P

Expert-verifiedFound in: Page 440

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**In the engine of a locomotive, a cylindrical piece known as a piston oscillates in SHM in a cylinder head (cylindrical chamber) with an angular frequency of 180 rev/min. Its stroke (twice the amplitude) is 0.76 m.What is its maximum speed?**

Its maximum speed is 7.2 m/s.

- Angular frequency of oscillation, .
- Stroke of the piston = 2Maximum displacement of piston, .

**A piston of an engine of a locomotive executes a Simple Harmonic Motion. Using the formula of the maximum velocity of a body in oscillation, we can get the speed.**

** **

Formula:

The maximum velocity of a body in oscillation, (i)

Conversion of rev/min to rad/sec,

(ii)

The first step will be to convert the angular frequency into the units of rad/s from the given rev/min.

Using the formula from equation (ii), we get the angular frequency as:

Also, the maximum displacement of the piston is given as:

For SHM, the maximum speed of oscillations using equation (i) and the given values is given by:

Hence, the value of the maximum speed is 7.2 m/s .

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