## ExerciseUse the values from PRACTICE IT to help you work through this exercise. Suppose the spring system in the last example starts at \( x = 0 \) and the attached object is given a kick to the right, so it has an initial speed of **0.64 m/s**.### (a)What distance from the origin does the object travel before coming to rest, assuming the surface is frictionless?- _____ m### (b)How does the answer change if the coefficient of kinetic friction is \( \mu_k = 0.120 \)? (Use the quadratic formula.)- _____ m**Hints:**- [Getting Started](#)- [I'm Stuck!](#) ---**PRACTICE IT**Use the worked example above to help you solve this problem. A block with a mass of **5.79 kg** is attached to a horizontal spring with a spring constant \( k = 3.32 \times 10^2 \, \text{N/m} \), as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to \( x_i = 0.0510 \, \text{m} \) and released.**(a)** Find the speed of the block at the equilibrium point. \_\_\_\_\_\_\_\_\_\_ m/s**(b)** Find the speed when \( x = 0.029 \, \text{m} \). \_\_\_\_\_\_\_\_\_\_ m/s**(c)** Repeat part (a) if friction acts on the block, with coefficient \( \mu_k = 0.120 \). \_\_\_\_\_\_\_\_\_\_ m/s---**Explanation of Diagram/Graph (if included):**The exercise refers to a conceptual setup involving a block attached to a spring. While the specific figure is not visible in the text, it likely depicts a spring-block system on a horizontal, frictionless surface, illustrating the initial displacement \( x_i \) and the block's motion back toward equilibrium.

Answered: Image /qna-images/answer/8455e4ad-308e-4377-8697-e916cd0e0a40.jpg

Use the values from PRACTICE IT to help you work this exercise. Suppose the spring system in the last example starts at x = 0 and the attached object is given a kick to the right, so it has an initial speed of 0.64 m/s. (a) What distance from the origin does the object travel before coming to rest, assuming the surface is frictionless? m (b) How does the answer change if the coefficient of kinetic friction is μ = 0.120? (Use the quadratic formula.) m

Use the values from PRACTICE IT to help you work this exercise. Suppose the spring system in the last example starts at x = 0 and the attached object is given a kick to the right, so it has an initial speed of 0.64 m/s. (a) What distance from the origin does the object travel before coming to rest, assuming the surface is frictionless? m (b) How does the answer change if the coefficient of kinetic friction is μ = 0.120? (Use the quadratic formula.) m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

## Exercise

Use the values from PRACTICE IT to help you work through this exercise. Suppose the spring system in the last example starts at \( x = 0 \) and the attached object is given a kick to the right, so it has an initial speed of **0.64 m/s**.

### (a)
What distance from the origin does the object travel before coming to rest, assuming the surface is frictionless?
- _____ m

### (b)
How does the answer change if the coefficient of kinetic friction is \( \mu_k = 0.120 \)? (Use the quadratic formula.)
- _____ m

**Hints:**
- [Getting Started](#)
- [I'm Stuck!](#)

---

**PRACTICE IT**

Use the worked example above to help you solve this problem. A block with a mass of **5.79 kg** is attached to a horizontal spring with a spring constant \( k = 3.32 \times 10^2 \, \text{N/m} \), as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to \( x_i = 0.0510 \, \text{m} \) and released.

**(a)** Find the speed of the block at the equilibrium point.
\_\_\_\_\_\_\_\_\_\_ m/s

**(b)** Find the speed when \( x = 0.029 \, \text{m} \).
\_\_\_\_\_\_\_\_\_\_ m/s

**(c)** Repeat part (a) if friction acts on the block, with coefficient \( \mu_k = 0.120 \).
\_\_\_\_\_\_\_\_\_\_ m/s

---

**Explanation of Diagram/Graph (if included):**

The exercise refers to a conceptual setup involving a block attached to a spring. While the specific figure is not visible in the text, it likely depicts a spring-block system on a horizontal, frictionless surface, illustrating the initial displacement \( x_i \) and the block's motion back toward equilibrium.

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