Physics for Scientists and Engineers, Technology Update (No access codes included)
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![**Question 4:** Rocker Rob enters from stage left at a speed of 5 m/s and slides to a rest over a distance of 2 m. What is the coefficient of kinetic friction between his socked-feet and the marley stage floor below?
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*Explanation for Educational Purposes:*
In this physics problem, we're asked to calculate the coefficient of kinetic friction. Here's how you can solve it:
1. **Identify the Given Data:**
- Initial velocity (v_i) = 5 m/s
- Final velocity (v_f) = 0 m/s (because he comes to rest)
- Distance (d) = 2 m
2. **Understand the Concept:**
- The kinetic friction opposes the motion, causing Rob to decelerate and eventually stop.
- Use the equation of motion and the relationship between frictional force and deceleration to find the coefficient of kinetic friction (\( \mu_k \)).
3. **Relevant Equations:**
- \( v_f^2 = v_i^2 + 2a \cdot d \)
- Force of friction \( f_k = \mu_k \cdot N \)
- \( f = m \cdot a \) (Newton's second law)
4. **Calculate the Deceleration:**
- Rearrange the first equation to find acceleration (a):
\[ 0 = (5 \, \text{m/s})^2 + 2a \cdot 2 \, \text{m} \]
\[ 0 = 25 + 4a \]
\[ a = -\frac{25}{4} \, \text{m/s}^2 = -6.25 \, \text{m/s}^2 \]
5. **Solve for the Coefficient of Kinetic Friction:**
- Assume normal force \( N = m \cdot g \) (where g = 9.8 m/s²). For simplification, mass (m) will cancel out:
- \( f_k = \mu_k \cdot mg = m \cdot a \)
- \(\mu_k \cdot g = -a\)
- \(\mu_k = \frac{-a}{g} = \frac{6.25}{9.8}\)
- \(\mu_k](https://content.bartleby.com/qna-images/question/4a2bd348-d826-4056-b9ee-5fd404bc60f1/7ec3322a-e79e-4187-83e5-3bacbfcabfdc/17xlr8_processed.jpeg)
Transcribed Image Text:**Question 4:** Rocker Rob enters from stage left at a speed of 5 m/s and slides to a rest over a distance of 2 m. What is the coefficient of kinetic friction between his socked-feet and the marley stage floor below?
---
*Explanation for Educational Purposes:*
In this physics problem, we're asked to calculate the coefficient of kinetic friction. Here's how you can solve it:
1. **Identify the Given Data:**
- Initial velocity (v_i) = 5 m/s
- Final velocity (v_f) = 0 m/s (because he comes to rest)
- Distance (d) = 2 m
2. **Understand the Concept:**
- The kinetic friction opposes the motion, causing Rob to decelerate and eventually stop.
- Use the equation of motion and the relationship between frictional force and deceleration to find the coefficient of kinetic friction (\( \mu_k \)).
3. **Relevant Equations:**
- \( v_f^2 = v_i^2 + 2a \cdot d \)
- Force of friction \( f_k = \mu_k \cdot N \)
- \( f = m \cdot a \) (Newton's second law)
4. **Calculate the Deceleration:**
- Rearrange the first equation to find acceleration (a):
\[ 0 = (5 \, \text{m/s})^2 + 2a \cdot 2 \, \text{m} \]
\[ 0 = 25 + 4a \]
\[ a = -\frac{25}{4} \, \text{m/s}^2 = -6.25 \, \text{m/s}^2 \]
5. **Solve for the Coefficient of Kinetic Friction:**
- Assume normal force \( N = m \cdot g \) (where g = 9.8 m/s²). For simplification, mass (m) will cancel out:
- \( f_k = \mu_k \cdot mg = m \cdot a \)
- \(\mu_k \cdot g = -a\)
- \(\mu_k = \frac{-a}{g} = \frac{6.25}{9.8}\)
- \(\mu_k
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