Explanation Given information: The radius of the cylinder is r . Calculation: Show the position of the particle inside the cylindrical surface as in Figure (1). Take the datum at position 2. For position 1: Write the expression for the displacement ( x ): x = R ( 1 − cos θ m ) Write the expression for kinetic energy ( T 1 ) : T 1 = 0 Write the expression for potential energy ( V 1 ) : V 1 = W x Substitute R ( 1 − cos θ m ) for x . V 1 = W R ( 1 − cos θ m ) ( 1 − cos θ m = 2 sin 2 θ m 2 ) = W R sin 2 θ m 2 For small oscillation sin θ ≈ θ . V 1 = W R θ m 2 2 For position 2. Write the expression maximum velocity ( v m ) : v m = R θ ˙ m Here, θ ˙ m is maximum angular velocity. Write the expression for kinetic energy ( T 2 ) : T 2 = 1 2 m v m 2 Substitute R θ ˙ m for v m . T 2 = 1 2 m ( R θ ˙ m ) 2 Write the expression for potential energy ( V 2 ) : V 2 = 0 Write the expression for weight ( W ): W = m g Write the expression for maximum angular velocity ( θ ˙ m ) :

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

See similar textbooks

Videos

Question

Chapter 19.3, Problem 19.72P

To determine

The period of small (τn) oscillation of a small particle which moves without friction inside a cylindrical surface of radius R.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.3, Problem 19.71P

Chapter 19.3, Problem 19.73P

Students have asked these similar questions

A 14-oz sphere A and a 10-oz sphere C are attached to the ends of a 20-oz rod AC are attached to the ends of a 20-oz rod B Determine the period of small oscillations of the rod.

A block of mass m = 400 g, is attached to a horizontal spring and set in simple harmonic motion as shown. At what point(s) in the motion is the velocity of the block at its maximum? ww X = -A O a. x = 0, and x = -A O b. x=0, x= -A, and x = -A O e. O c. O d. x = 0 x = -A, and x = +A . x = 0, and x = +A m x = 0 X = +A

Answer the following regarding mass:

Chapter 19 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The period of small ( τ n ) oscillation of a small particle which moves without friction inside a cylindrical surface of radius R .

Solution Summary: The author calculates the period of small oscillation of a small particle which moves without friction inside the cylindrical surface of radius R.

Videos

The period of small (τn) oscillation of a small particle which moves without friction inside a cylindrical surface of radius R.

Want to see the full answer?

Chapter 19 Solutions