### Understanding the Conservation of Energy in a System with Conservative Forces#### Problem Statement:When only conservative forces act on a system, the conservation of energy theorem can be utilized to solve problems effectively. For particle kinetics, the principle is expressed as:\[ T_1 + V_1 = T_2 + V_2 \]where \( T \) represents kinetic energy and \( V \) signifies potential energy, comprising gravitational potential energy (\( V_g \)) and elastic potential energy (\( V_e \)).#### Given Data:- The potential energy contributions are \( V_g = Wy_c \) (gravitational potential energy) and \( V_e = \frac{1}{2} k s^2 \) (elastic potential energy).- A rod with a mass of 30 kg is released from rest at an angle \(\theta = 45^\circ\).- The spring is unstretched when \(\theta = 45^\circ\).- The goal is to determine the angular velocity of the rod when \(\theta = 0^\circ\) using the conservation of energy theorem.#### System Description:- The rod \( AB \) is 1.5 meters in length.- The spring constant \( k \) is \( 300 \, \text{N/m} \).- The initial conditions (position and rest state) are specified for \(\theta = 45^\circ\).### Diagram Explanation:The accompanying diagram shows:- A rod \( AB \) attached to a fixed point at \( B \).- An unstretched spring connected to the rod at point \( A \) when \(\theta = 45^\circ\).- The rod is positioned at an angle \(\theta\) from the horizontal, initially set to \( 45^\circ\).- The length of the rod is marked as 1.5 meters, illustrating its pivot and the extension mechanism of the spring as the angle changes.### Objective:By leveraging the conservation of energy theorem, one can find the angular velocity of the rod when \(\theta\) is \(0^\circ\). This process involves:1. Calculating the initial potential energy due to both gravity and spring elasticity when \(\theta = 45^\circ\).2. Determining the final potential energy at \(\theta = 0^\circ\).3. Using the difference in potential energies to uphold the conservation of energy principle and

Answered: Image /qna-images/answer/8d771f7b-0247-4f69-8e66-e19db11fbcd8.jpg

Answered: determine the angular velocity of the…

Engineering

Mechanical Engineering

determine the angular velocity of the rod when 0 = 0°.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: Determine the angular velocity of link BC at the instant shown

A: To find: The angular velocity of link BC = ?

Q: Point A is moving downward at 5 m/s. When θ= 45 ° determine, the angular velocity of the bar AB, the…

A: The point A is moving downward is given as, vA=5 m/s The angle of bar is given as,θ=45∘ The length…

Q: link lengths for a fourbar slider mechanism are: a = 2.8 cm and b = 8 cm. If w2 = 60 rad/s,…

Q: If the bar has a clockwise angular velocity of 10 rad/s and v of its instantaneous center of the…

Q: 0.3 m 0.3 m В E 0.6 m OcD = 6 rad/s 30° D

A: Given Data WCD=6 rad/s

Q: öf the gear, and (b) the acceleration of points B,C, and D. s stationary, Determ B. VA 2.5 m/s D a=4…

Q: The pinion gear rolls on the gear racks. If B is moving to the right at 8 ft/s and C is moving to…

A: Given: r = 0.3 ft VB = 8 ft/s VA = - 4 ft/s

Q: Q1/ The double gear shown rolls on the stationary lower rack; the velocity of its center A is 1.6…

A: for the given arrangement vA = 1.6 m/s r1 = 175 mm r2 = 125 mm To determine Angular velocity…

Q: The ends of the 0.62-m bar remain in contact with their respective support surfaces. End B has a…

Q: Please display all work

A: Given information: - The wheel has a radius of 4 inches. - The wheel is rolling to the left with a…

Q: If rod CD is rotating with an angular velocity wCD. At the instant shown in the figure, which letter…

Q: Problem 4. The disk shown here rolls without slipping such that at the instant shown it has an…

Q: 3) At the instant show, the velocity of point A of the 1.2 m bar is 3 m/s to the right. Determine…

A: Speed of point BvB=4.37m/sAngular velocity of rod ωrod=3.23rad/sExplanation:Explanation

Q: 16-65. The pinion gear rolls on the gear racks. If B is moving to the right at 8 ft/s and C is…

Q: Detemine the angular velocity of the link CB at the instant shown measured clockwise, if the link AB…

Q: The plate gears A and B are rotating with the angular velocities ωA = 6 rad/srad/s and ωB = 18…

A: Angular veocity of gear A, ωA=6 rad/sAngular velocity of gear B, ωB=18 rad/s

Q: t. 16-77. The planetary gear system is used in an automatic transmission for an automobile. By…

Q: In the image on the right, there is a red gear G1 on the left with a radius of r1 = 2.81cm. Gear G1…

Q: Disc A rotates at 500 rpm in a counterclockwise direction. When θ = 45 ° and rod BD is 9 inches…

A: There are two types of forces that are acting on a circular surface. One type of force is Radial…

Q: y b k.. a

A: Diameter of the part= a Diameter of the hole= c Distance between top edge of the part and top edge…

Q: If roller A moves to the right with a constant velocity of VA = 3 m/s, determine the angular…

A: Given data:- Velocity of vA = 3 m/s Length of AB=1.5 m θ=30°. To find:-the angular velocity of the…

Q: 1. In the mechanism on the right, link BC is horizontal at the instant 0 = 60°. If @aB = 10 rad/s…

Q: If the hydraulic cylinder shortens at a constant rate of 4 ft/s, determine the angular velocity of…

A: Free-Body Diagram:

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

### Understanding the Conservation of Energy in a System with Conservative Forces

#### Problem Statement:
When only conservative forces act on a system, the conservation of energy theorem can be utilized to solve problems effectively. For particle kinetics, the principle is expressed as:

\[ T_1 + V_1 = T_2 + V_2 \]

where \( T \) represents kinetic energy and \( V \) signifies potential energy, comprising gravitational potential energy (\( V_g \)) and elastic potential energy (\( V_e \)).

#### Given Data:
- The potential energy contributions are \( V_g = Wy_c \) (gravitational potential energy) and \( V_e = \frac{1}{2} k s^2 \) (elastic potential energy).
- A rod with a mass of 30 kg is released from rest at an angle \(\theta = 45^\circ\).
- The spring is unstretched when \(\theta = 45^\circ\).
- The goal is to determine the angular velocity of the rod when \(\theta = 0^\circ\) using the conservation of energy theorem.

#### System Description:
- The rod \( AB \) is 1.5 meters in length.
- The spring constant \( k \) is \( 300 \, \text{N/m} \).
- The initial conditions (position and rest state) are specified for \(\theta = 45^\circ\).

### Diagram Explanation:
The accompanying diagram shows:
- A rod \( AB \) attached to a fixed point at \( B \).
- An unstretched spring connected to the rod at point \( A \) when \(\theta = 45^\circ\).
- The rod is positioned at an angle \(\theta\) from the horizontal, initially set to \( 45^\circ\).
- The length of the rod is marked as 1.5 meters, illustrating its pivot and the extension mechanism of the spring as the angle changes.

### Objective:
By leveraging the conservation of energy theorem, one can find the angular velocity of the rod when \(\theta\) is \(0^\circ\).

This process involves:
1. Calculating the initial potential energy due to both gravity and spring elasticity when \(\theta = 45^\circ\).
2. Determining the final potential energy at \(\theta = 0^\circ\).
3. Using the difference in potential energies to uphold the conservation of energy principle and

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Diagram and other calculation

VIEW

Step 2: The angular velocity

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

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.

Similar questions

The differential pinion meshes on the two racks. If these move with the velocities shown, determine the angular velocity of the pinion and the velocity of its center C. 0.6 m/s 0.8 m/s 90 mm 150 mm
Draw FBD and determine the number of revolutions done by Disk E at thesame time.
4
3 moving to the right at 8 ft/s and C is moving to the left at 4 ft/s, determine the angular velocity of the pinion gear and the velocity of its center A. The pinion gear rolls on the gear racks. If B is C A_ 0.3 ft В
The ends of the 0.63-m bar remain in contact with their respective support surfaces. End B has a velocity of 0.40 m/s and an acceleration of 0.47 m/s² in the directions shown. Determine the angular acceleration a (positive if counterclockwise, negative if clockwise) of the bar and the acceleration of end A (positive if up, negative if down). 28 105 Answers: a = aA i i 0.63 m B 0.274 0.196 -ag=0.47m/s² UB=0.40 m/s rad/s² m/s²
υο VA W= A r v B CC A gear sits between two moving racks. If the top rack moves at a velocity of v₁ = 0.85 m/s to the left and the bottom rack moves at a velocity of VB = 0.3 m/s to the right, determine the velocity at the center of the gear, the magnitude of the angular velocity of the gear, and the distance to the ICZV from point B. The gear has a radius of r = 0.08 m. m/s Select an answer rad/s Select an answer VB BY UBC Engineering
C16-3. The bi-fold hangar door is opened by cables that move upward at a constant speed of 0.5 m/s. Determine the angular velocity of BC and the angular velocity of AB when e = 45°. Panel BC is pinned at C and has a height which is the same as the height of BA. Use appropriate numerical values to explain your result.
Rod CD rotates with an angular velocity of wcD = 3.23 rad/s as shown. Determine the angular velocity of rods AB and BC. Note: USE Instantaneous Center method only. B OCD= (2+EFG/100) rad/s C D 45° 1.5 m 60° 1 m A 1 m
In reference to the figure, WAB B B Given: AB = 10.5 m BC = 8.2 m 0 = 41° ß = 28° Determine the angular velocity in rad/s of link AB at the instant shown if block C is moving upward at 26 m/s. Express the final answer in 3 significant digits.
The rod AB has a mass of 36 kg and a length of 1.9m. The spring is unstretched when 0- 45°. The spring constant k is 226 N/m. B Find the angular velocity of rod AB at 0 - 0. if the rod is released from rest when 0. 45°. Give your answer with 2 decimals.
16-5. The operation of reverse gear in an automotive transmission is shown. If the engine turns shaft A at -40 rad/s, determine the angular velocity of the drive shaft, w,. The radius of cach gear is listed in the figure. 40 rad s 70 mm Prob. 16-5