A mass m = 11 kg rests on a frictionless table and accelerated by a spring with spring constant k = 4119 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is Hk = 0.53. The mass leaves the spring at a speed v = 3.9 m/s. 1) How much work is done by the spring as it accelerates the mass? J Submit 2) How far was the spring stretched from its unstreched length? Submit 3) The mass is measured to leave the rough spot with a final speed vf = 2.1 m/s. How much work is done by friction as the mass crosses the rough spot? J Submit

A mass m = 11 kg rests on a frictionless table and accelerated by a spring with spring constant k = 4119 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is Hk = 0.53. The mass leaves the spring at a speed v = 3.9 m/s. 1) How much work is done by the spring as it accelerates the mass? J Submit 2) How far was the spring stretched from its unstreched length? Submit 3) The mass is measured to leave the rough spot with a final speed vf = 2.1 m/s. How much work is done by friction as the mass crosses the rough spot? J Submit

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter7: Energy Of A System

Section: Chapter Questions

Problem 48AP

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Question

Can you please answer these

**Spring and Friction Problem**

A mass \( m = 11 \, \text{kg} \) rests on a frictionless table and is accelerated by a spring with a spring constant \( k = 4119 \, \text{N/m} \). The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is \( \mu_k = 0.53 \). The mass leaves the spring at a speed \( v = 3.9 \, \text{m/s} \).

### Questions:

1) **How much work is done by the spring as it accelerates the mass?**

\[
\text{[Input box]} \, \text{J} \quad \text{Submit}
\]

2) **How far was the spring stretched from its unstretched length?**

\[
\text{[Input box]} \, \text{m} \quad \text{Submit}
\]

3) **The mass is measured to leave the rough spot with a final speed \( v_f = 2.1 \, \text{m/s} \). How much work is done by friction as the mass crosses the rough spot?**

\[
\text{[Input box]} \, \text{J} \quad \text{Submit}
\]

4) **What is the length of the rough spot?**

\[
\text{[Input box]} \, \text{m} \quad \text{Submit}
\]

5) In a new scenario, the block only makes it (exactly) halfway through the rough spot. How far was the spring compressed from its unstretched length?

[Text Box] m Submit

---

6) In this new scenario, what would the coefficient of friction of the rough patch need to be changed to in order for the block to just barely make it through the rough patch?

[Text Box] Submit

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