**Problem Description:** The wheel is attached to a spring. The parameters and conditions of the system are given as follows: - Mass of the wheel: \( m = 20 \, \text{kg} \) - Radius of the wheel: \( r = 0.6 \, \text{m} \) - Radius of gyration: \( k_G = 0.4 \, \text{m} \) - Spring’s unstretched length: \( L_0 = 1.0 \, \text{m} \) - Stiffness coefficient of the spring: \( k = 2.0 \, \text{N/m} \) **System Behavior:** 1. The wheel is released from rest at State 1. 2. At State 1, the angle between the spring and the vertical direction is \( \theta = 30^\circ \). 3. The wheel rolls without slipping and reaches State 2 when \( \theta = 0^\circ \). 4. The spring’s length at State 2 is \( L_2 = 4 \, \text{m} \). **Question:** Determine the kinetic energy at State 1. Provide the answer in Newton-meters (N-m) using two decimal places. **Diagram Explanation:** - The diagram illustrates two states of a system where a wheel is connected to a spring. - At State 1, the wheel is positioned at an angle of \( 30^\circ \) from the vertical, indicating initial potential energy stored in the spring and potential energy due to height. - At State 2, the wheel has moved to an angle of \( 0^\circ \) where the spring is further extended. The task is to calculate the kinetic energy at State 1 based on these conditions and the properties of the system.
**Problem Description:** The wheel is attached to a spring. The parameters and conditions of the system are given as follows: - Mass of the wheel: \( m = 20 \, \text{kg} \) - Radius of the wheel: \( r = 0.6 \, \text{m} \) - Radius of gyration: \( k_G = 0.4 \, \text{m} \) - Spring’s unstretched length: \( L_0 = 1.0 \, \text{m} \) - Stiffness coefficient of the spring: \( k = 2.0 \, \text{N/m} \) **System Behavior:** 1. The wheel is released from rest at State 1. 2. At State 1, the angle between the spring and the vertical direction is \( \theta = 30^\circ \). 3. The wheel rolls without slipping and reaches State 2 when \( \theta = 0^\circ \). 4. The spring’s length at State 2 is \( L_2 = 4 \, \text{m} \). **Question:** Determine the kinetic energy at State 1. Provide the answer in Newton-meters (N-m) using two decimal places. **Diagram Explanation:** - The diagram illustrates two states of a system where a wheel is connected to a spring. - At State 1, the wheel is positioned at an angle of \( 30^\circ \) from the vertical, indicating initial potential energy stored in the spring and potential energy due to height. - At State 2, the wheel has moved to an angle of \( 0^\circ \) where the spring is further extended. The task is to calculate the kinetic energy at State 1 based on these conditions and the properties of the system.
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Question
The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m.
(10) The kinetic energy at the state1?________ (N·m) (two decimal places)
Transcribed Image Text:**Problem Description:**
The wheel is attached to a spring. The parameters and conditions of the system are given as follows:
- Mass of the wheel: \( m = 20 \, \text{kg} \)
- Radius of the wheel: \( r = 0.6 \, \text{m} \)
- Radius of gyration: \( k_G = 0.4 \, \text{m} \)
- Spring’s unstretched length: \( L_0 = 1.0 \, \text{m} \)
- Stiffness coefficient of the spring: \( k = 2.0 \, \text{N/m} \)
**System Behavior:**
1. The wheel is released from rest at State 1.
2. At State 1, the angle between the spring and the vertical direction is \( \theta = 30^\circ \).
3. The wheel rolls without slipping and reaches State 2 when \( \theta = 0^\circ \).
4. The spring’s length at State 2 is \( L_2 = 4 \, \text{m} \).
**Question:**
Determine the kinetic energy at State 1. Provide the answer in Newton-meters (N-m) using two decimal places.
**Diagram Explanation:**
- The diagram illustrates two states of a system where a wheel is connected to a spring.
- At State 1, the wheel is positioned at an angle of \( 30^\circ \) from the vertical, indicating initial potential energy stored in the spring and potential energy due to height.
- At State 2, the wheel has moved to an angle of \( 0^\circ \) where the spring is further extended.
The task is to calculate the kinetic energy at State 1 based on these conditions and the properties of the system.
Expert Solution
Step 1 To determine,
The kinetic energy at the state1.
Given,
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