**LEARN MORE****REMARKS** Friction or drag from immersion in a fluid damps the motion of an object attached to a spring, eventually bringing the object to rest.**QUESTION** In the case of friction, what percent of the mechanical energy was lost by the time the mass first reached the equilibrium point? (*Hint: use the answers to parts (a) and (c).*)[Input Box] %---**PRACTICE IT**Use the worked example above to help you solve this problem. A block with mass of **5.79 kg** is attached to a horizontal spring with spring constant **k = 3.32 x 10² N/m**, as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to **xᵢ = 0.0510 m** and released.(a) Find the speed of the block at the equilibrium point. [Input Box] m/s(b) Find the speed when **x = 0.029 m**. [Input Box] m/s(c) Repeat part (a) if friction acts on the block, with coefficient **μₖ = 0.120**. [Input Box] m/s **Educational Content: Analyzing the Speed of a Block on a Spring****Introduction to the Problem:**The problem involves analyzing the speed of a block attached to a spring using the principles of kinetic and potential energy. The exercise is divided into three parts: without friction, at the halfway point, and with friction.---**(A) Initial Scenario: No Friction**1. **Equation Setup:** - Start by applying the conservation of energy principle: \[ \frac{1}{2} mv_i^2 + \frac{1}{2} k x_i^2 = \frac{1}{2} mv_f^2 + \frac{1}{2} k x_f^2 \] - Initial speed \( v_i \) is 0, final position \( x_f \) is 0.2. **Calculation:** - Substitute and multiply by \( 2/m \): \[ \frac{k}{m} x_i^2 = v_f^2 \] - Solve for \( v_f \): \[ v_f = \sqrt{\frac{k}{m} x_i} \] - Using given values: \[ v_f = \sqrt{\frac{4.00 \times 10^2 \, \text{N/m}}{5.00 \, \text{kg}} (0.0500 \, \text{m})} \] \[ v_f = 0.447 \, \text{m/s} \]---**(B) At the Halfway Point:**1. **Equation Setup:** - Position \( x = 0.025 \, \text{m} \): \[ \frac{k x_i^2}{m} = v_f^2 + \frac{k x_f^2}{m} \]2. **Calculation:** - Solve for \( v_f \): \[ v_f = \sqrt{\frac{k}{m} (x_i^2 - x_f^2)} \] - Using given values: \[ v_f = \sqrt{\frac{4.00 \times 10^2 \, \text{N/m}}{5.00 \, \text{kg}} [(0.050 \, \text{m})^2 - (0.

Answered: Image /qna-images/answer/3471bac2-bd8f-49e6-bb74-08ef152a0edd.jpg

Use the worked example above to help you solve this problem. A block with mass of 5.79 kg is attached to a horizontal spring with spring constant k = 3.32 x 10² N/m, as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to x; = 0.0510 m and released. (a) Find the speed of the block at the equilibrium point. m/s (b) Find the speed when x = 0.029 m. m/s (c) Repeat part (a) if friction acts on the block, with coefficient μ = 0.120.

Use the worked example above to help you solve this problem. A block with mass of 5.79 kg is attached to a horizontal spring with spring constant k = 3.32 x 10² N/m, as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to x; = 0.0510 m and released. (a) Find the speed of the block at the equilibrium point. m/s (b) Find the speed when x = 0.029 m. m/s (c) Repeat part (a) if friction acts on the block, with coefficient μ = 0.120.

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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Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

**LEARN MORE**

**REMARKS**
Friction or drag from immersion in a fluid damps the motion of an object attached to a spring, eventually bringing the object to rest.

**QUESTION**
In the case of friction, what percent of the mechanical energy was lost by the time the mass first reached the equilibrium point? (*Hint: use the answers to parts (a) and (c).*)

[Input Box] %

---

**PRACTICE IT**

Use the worked example above to help you solve this problem. A block with mass of **5.79 kg** is attached to a horizontal spring with spring constant **k = 3.32 x 10² N/m**, as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to **xᵢ = 0.0510 m** and released.

(a) Find the speed of the block at the equilibrium point.
[Input Box] m/s

(b) Find the speed when **x = 0.029 m**.
[Input Box] m/s

(c) Repeat part (a) if friction acts on the block, with coefficient **μₖ = 0.120**.
[Input Box] m/s

**Educational Content: Analyzing the Speed of a Block on a Spring**

**Introduction to the Problem:**
The problem involves analyzing the speed of a block attached to a spring using the principles of kinetic and potential energy. The exercise is divided into three parts: without friction, at the halfway point, and with friction.

---

**(A) Initial Scenario: No Friction**

1. **Equation Setup:**
- Start by applying the conservation of energy principle:
\[ \frac{1}{2} mv_i^2 + \frac{1}{2} k x_i^2 = \frac{1}{2} mv_f^2 + \frac{1}{2} k x_f^2 \]
- Initial speed \( v_i \) is 0, final position \( x_f \) is 0.

2. **Calculation:**
- Substitute and multiply by \( 2/m \):
\[ \frac{k}{m} x_i^2 = v_f^2 \]
- Solve for \( v_f \):
\[ v_f = \sqrt{\frac{k}{m} x_i} \]
- Using given values:
\[ v_f = \sqrt{\frac{4.00 \times 10^2 \, \text{N/m}}{5.00 \, \text{kg}} (0.0500 \, \text{m})} \]
\[ v_f = 0.447 \, \text{m/s} \]

---

**(B) At the Halfway Point:**

1. **Equation Setup:**
- Position \( x = 0.025 \, \text{m} \):
\[ \frac{k x_i^2}{m} = v_f^2 + \frac{k x_f^2}{m} \]

2. **Calculation:**
- Solve for \( v_f \):
\[ v_f = \sqrt{\frac{k}{m} (x_i^2 - x_f^2)} \]
- Using given values:
\[ v_f = \sqrt{\frac{4.00 \times 10^2 \, \text{N/m}}{5.00 \, \text{kg}} [(0.050 \, \text{m})^2 - (0.

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