Transcription for Educational Website --- The wheel is attached to the spring. The mass of the wheel is $ m = 20 \, \text{kg} $. The radius of the wheel is $ 0.6 \, \text{m} $. The radius of gyration $ k_g = 0.4 \, \text{m} $. The spring's unstretched length is $ L_0 = 1.0 \, \text{m} $. The stiffness coefficient of the spring is $ k = 2.0 \, \text{N/m} $. The wheel is released from rest at state 1 when the angle between the spring and the vertical direction is $ \theta = 30^\circ $. The wheel rolls without slipping and passes the position at the state 2 when the angle is $ \theta = 0^\circ $. The spring's length at state 2 is $ L_2 = 4 \, \text{m} $. (5) The stretched spring length of the spring at the state 2 is _______ $ \text{m} $ (two decimal places). Diagram Explanation: The diagram displays two states of a spring-wheel system. - State 1: - The spring is at an angle ($\theta = 30^\circ$) from the vertical. - The initial length $ L_0 $ of the spring is visibly shorter than in state 2. - State 2: - The spring is vertically aligned ($\theta = 0^\circ$). - The length $ L_2 = 4 \, \text{m} $ is indicated, showing the extended length of the spring. Arrows and lines annotate the spring's length and the angle changes in both states, demonstrating the spring's extension due to the wheel's motion.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter8: Centroids And Distributed Loads

Section: Chapter Questions

Problem 8.73P

See similar textbooks

Related questions

Question

**Transcription for Educational Website**

---

The wheel is attached to the spring. The mass of the wheel is $ m = 20 \, \text{kg} $. The radius of the wheel is $ 0.6 \, \text{m} $. The radius of gyration $ k_g = 0.4 \, \text{m} $. The spring's unstretched length is $ L_0 = 1.0 \, \text{m} $.

The stiffness coefficient of the spring is $ k = 2.0 \, \text{N/m} $. The wheel is released from rest at state 1 when the angle between the spring and the vertical direction is $ \theta = 30^\circ $. The wheel rolls without slipping and passes the position at the state 2 when the angle is $ \theta = 0^\circ $. The spring's length at state 2 is $ L_2 = 4 \, \text{m} $.

**(5)** The stretched spring length of the spring at the state 2 is _______ $ \text{m} $ (two decimal places).

**Diagram Explanation:**

The diagram displays two states of a spring-wheel system.

- **State 1:**
- The spring is at an angle ($\theta = 30^\circ$) from the vertical.
- The initial length $ L_0 $ of the spring is visibly shorter than in state 2.

- **State 2:**
- The spring is vertically aligned ($\theta = 0^\circ$).
- The length $ L_2 = 4 \, \text{m} $ is indicated, showing the extended length of the spring.

Arrows and lines annotate the spring's length and the angle changes in both states, demonstrating the spring's extension due to the wheel's motion.

Expert Solution

Step 1

Given Data:

Mass of wheel $M_{m a s s} = 20 kg$

Radius of wheel $R_{W h e e l} = 0.6 m$

Radius of gyration $K_{G} = 0.4 m$

Unstretched length of spring $L_{0} = 1 m$

Stiffness coefficient of spring $k = 2 \frac{N}{m}$

Length of spring at state 2 $L_{2} = 4 m$

Step by step

Solved in 2 steps

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.