Page 83 - C:\Users\trainee\AppData\Local\Temp\msoEAA3.tmp

Document Title
Fundamentals of Stress and Vibration 2. Engineering Mechanics Chapter
[A Practical guide for aspiring Designers / Analysts]

Since we know that, ‘a’ is greater than ‘b’ (‘a’ being the major axis), the radius of curvature is
maximum at ‘B’ and ‘D’ and minimum at ‘A’ and ‘C’.

Hence, the ratio of minimum and maximum centripetal acceleration given by:

v 2 b 2
Centripetal acceleration minimum R R max a b 2 b b 3
= min = = = ∗ =
2
Centripetal acceleration maximum v 2 R min a a 2 a 3
a
R max b
Example 2: a cylinder when at the top of a hemisphere, is given a small perturbance, to which,
the cylinder starts rolling down. Compute the angle ‘θ’ at which the cylinder loses contact with the
hemisphere. Assume that, friction is absent, and the hemisphere is firmly fixed to the ground.

[Fig 2.70: cylinder rolling down a hemisphere]

Solution: as the cylinder rolls down, the kinetic energy increases and so does the centrifugal
force, as shown in [Fig 2.71]. At one point, the contact is lost, where, the weight component of the
cylinder, which provides the contact reaction is reduced to zero.

[Fig 2.71: cylinder rolling down a hemisphere]

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 83 age 83
P
Copyright Diary No – 9119/2018-CO/L