### Understanding the Motion of a Block Sliding Along a Smooth Cylindrical Surface#### Problem StatementThe 2-lb block is released from rest at point \( A \) and slides down along the smooth cylindrical surface. The attached spring has a stiffness \( k = 3 \) lb/ft. (Figure 1)#### Detailed Diagram ExplanationThe accompanying figure illustrates a block of weight 2 pounds positioned initially at point \( A \) atop a smooth cylindrical surface. The surface is delineated as a semi-circle with a radius of 2 feet.- **Block at Point A:** The block starts at position \( A \), which is at the top of the semi-circular plane.- **Spring Attachment:** Attached to the block is a spring that extends from a fixed point at the bottom center of the semicircle (the origin) to the block. The spring is depicted as a helical spring.- **Angle \( \theta \) Representation:** The angle \( \theta \) is formed between the vertical line from the center to point \( A \) and the line from the center of the semicircle to the current position of the block as it slides down.- **Spring Stiffness:** The spring has a stiffness constant denoted by \( k \), which is equal to 3 lb/ft.This model is used to analyze the mechanics of how a weighted block interacts with a spring system as it traverses a smooth cylindrical surface under the influence of gravity. ### Problem Statement: Part A**Task:**Determine its unstretched length so that it does not allow the block to leave the surface until \( \theta = 60^\circ \). **Instructions:**Express your answer to three significant figures and include the appropriate units.**Input Field:**An input field is provided to enter the unstretched length \( l_0 \). For example, in the image, the input is:\[ l_0 = 1.58 \, \text{ft} \]**Submission:**Click the "Submit" button to check your answer.**Feedback Section:**After submission, feedback is provided. In this example, the feedback indicates:\[ \text{Incorrect; Try Again; 3 attempts remaining} \]Additionally, options for "Previous Answers" and "Request Answer" are available for reference.Please ensure you follow these guidelines to correctly format your response and avoid mistakes.

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Answered: The 2-1b block is released from rest at…

The 2-1b block is released from rest at A slides down along the smooth cylindrical surface. The attached spring has a stiffness k = 3 lb/ft. (Figure 1)

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 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. (8) The mass moment of inertial about the mass center G is IG =_________(kg·m2 ) (two decimal places)
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 Lo=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 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 0-0°. The spring's length at the state 2 is L2=4 m. (12) The kinetic energy at the state 2? (N-m) (two decimal places) LLLLKAL 2₂ तो State 2 Li State 1
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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 Lo=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 0-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 8=0°. The spring's length at the state 2 is L2=4 m. (kg-m²) (two (8) The mass moment of inertial about the mass center G is IG= decimal places) HILAI L₂ State 2 State 1
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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. (9) The mass moment of inertial about the IC center is IIC =_________(kg·m2 ) (two decimal places)
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