Explanation Given information: A uniform rod AB can rotate in a vertical plane about a horizontal axis at C located at a distance c above the mass center G of the rod. Calculations: From the figure shown above: k i n e t i c e n e r g y a t p o s i t i o n 1 : T 1 = 0 P o t e n t i o l e n e r g y a t p o s i t i o n 1 : V 1 = m g h w h e r e , h = c ( 1 − cos θ m ) V 1 = m g c ( 1 − cos θ m ) [ 1 − cos θ m = 2 sin 2 θ m 2 f o r s m a l l v a l u e o f θ m ; 1 − cos θ m ≈ 2 ( θ m 2 ) 2 = θ m 2 2 ] ∴ V 1 = m g c θ 2 m 2 A t P o s i t i o n 2 : k i n e t i c e n e r g y a t P o s i t i o n 2 : T 2 = 1 2 I C θ . m 2 w h e r e , I C → M o m e n t o f i n e r t i a o f t h e r o d a b o u t p o int C ( I C = I ¯ + m c 2 = 1 12 m l 2 + m c 2 ) ∴ T 2 = 1 2 m ( l 2 12 + c 2 ) θ

12th Edition

ISBN: 9781260265521

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Gen…

Videos

Question

Chapter 19.3, Problem 19.75P

To determine

The value of C for which the frequency of the motion will be maximum.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.3, Problem 19.74P

Chapter 19.3, Problem 19.76P

Students have asked these similar questions

Uppgift 2 (9p) I77777 20 kN 10 kN/m 4 [m] 2 2 Bestäm tvärkrafts- och momentdiagram för balken i figuren ovan. Extrempunkter ska anges med både läge och värde i diagrammen.

**Problem 8-45.** The man has a mass of 60 kg and the crate has a mass of 100 kg. If the coefficient of static friction between his shoes and the ground is \( \mu_s = 0.4 \) and between the crate and the ground is \( \mu_c = 0.3 \), determine if the man is able to move the crate using the rope-and-pulley system shown. **Diagram Explanation:** The diagram illustrates a scenario where a man is attempting to pull a crate using a rope-and-pulley system. The setup is as follows: - **Crate (C):** Positioned on the ground with a rope attached. - **Rope:** Connects the crate to a pulley system and extends to the man. - **Pulley on Tree:** The rope runs over a pulley mounted on a tree which redirects the rope. - **Angles:** - The rope between the crate and tree forms a \(30^\circ\) angle with the horizontal. - The rope between the tree and the man makes a \(45^\circ\) angle with the horizontal. - **Man (A):** Pulling on the rope with the intention of moving the crate. This arrangement tests the…

please solve this problems follow what the question are asking to do please show me step by step

Chapter 19 Solutions

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS

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 - A 20-lb block is initially held so that the...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 - A 5-kg fragile glass vase is surrounded by packing...

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 value of C for which the frequency of the motion will be maximum.

Solution Summary: The author calculates the value of C for which the frequency of the motion will be maximum.

Concept explainers

Videos

The value of C for which the frequency of the motion will be maximum.

Want to see the full answer?

Chapter 19 Solutions