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 is $ 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 the 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 = 60^\circ $. The spring’s length at the state 2 is $ L_2 = 4 \, \text{m} $. (3) The stretched spring length of the spring at the state 1 is \_\_\_\_\_\_ (m) (two decimal places): Diagram Explanation: The diagram shows two states of the system: - State 1: The wheel is at the initial position with the spring stretched to length $ L_1 $, and the angle $ \theta $ is $ 30^\circ $. - State 2: The wheel has rolled to a new position with the angle $ \theta $ now $ 60^\circ $ and the spring stretched to length $ L_2 = 4 \, \text{m} $. Both states depict the connection between the spring and the wheel, indicating the changes in spring length (from $ L_0 $ to $ L_1 $ and $ L_2 $) as the wheel rolls.

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

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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 is $ 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 the 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 = 60^\circ $. The spring’s length at the state 2 is $ L_2 = 4 \, \text{m} $.

**(3) The stretched spring length of the spring at the state 1 is \_\_\_\_\_\_ (m) (two decimal places):**

**Diagram Explanation:**
The diagram shows two states of the system:

- **State 1:** The wheel is at the initial position with the spring stretched to length $ L_1 $, and the angle $ \theta $ is $ 30^\circ $.
- **State 2:** The wheel has rolled to a new position with the angle $ \theta $ now $ 60^\circ $ and the spring stretched to length $ L_2 = 4 \, \text{m} $.

Both states depict the connection between the spring and the wheel, indicating the changes in spring length (from $ L_0 $ to $ L_1 $ and $ L_2 $) as the wheel rolls.

Expert Solution

Step 1 Given data.

According to question:-

$\begin{array}{rcl} m a s s o f t h e w h e e l (m) & = & 20 k g \\ r a d i u s o f w h e e l (r) & = & 0.6 m \\ r a d i u s o f g y r a t i o n (k_{G}) & = & 0.4 m \\ u n s t r e t c h e d l e n g t h o f s p r i n g (L_{0}) & = & 1 m \\ s p r i n g c o n s \tan t (k) & = & 2 N / m \\ A n g l e o f d e f l e c t i o n (θ) & = & 30 ° \\ S p r i n g l e n g t h a t s t a t e 2 (L_{2}) & = & 4 m \end{array}$

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