Q6)A 2.4kg book is resting on a horizontal desk. The coefficients of static and kinetic friction between the book and the table are 0.45 and 0.34 correspondingly. If a spring with spring constant of 48N/m pulls horizontally on the book, moving it across the table with a constant forward velocity of 0.47 m/s, how much does the spring stretch?

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**Physics Problem on Friction and Spring Constant**

**Problem Statement:**
A 2.4 kg book is resting on a horizontal desk. The coefficients of static and kinetic friction between the book and the table are 0.45 and 0.34, respectively. If a spring with a spring constant of 48 N/m pulls horizontally on the book, moving it across the table with a constant forward velocity of 4.7 m/s, how much does the spring stretch?

**Given Values:**
- Mass \( m = 2.4 \, \text{kg} \)
- Coefficient of kinetic friction \( \mu_k = 0.34 \)
- Coefficient of static friction \( \mu_s = 0.45 \)
- Spring constant \( k = 48 \, \text{N/m} \)
- Velocity \( v = 4.7 \, \text{m/s} \)

**Solution Approach:**
1. Calculate the normal force.
2. Determine the force of kinetic friction.
3. Use Hooke’s Law to find the spring stretch required to overcome friction.

The solution involves applying Newton’s laws and understanding the relationship between friction, spring force, and motion.

**Note:**
This exercise integrates concepts from mechanics, including frictional forces and Elasticity (spring behavior). Solving this problem will enhance your understanding of these principles in practical scenarios.
Transcribed Image Text:**Physics Problem on Friction and Spring Constant** **Problem Statement:** A 2.4 kg book is resting on a horizontal desk. The coefficients of static and kinetic friction between the book and the table are 0.45 and 0.34, respectively. If a spring with a spring constant of 48 N/m pulls horizontally on the book, moving it across the table with a constant forward velocity of 4.7 m/s, how much does the spring stretch? **Given Values:** - Mass \( m = 2.4 \, \text{kg} \) - Coefficient of kinetic friction \( \mu_k = 0.34 \) - Coefficient of static friction \( \mu_s = 0.45 \) - Spring constant \( k = 48 \, \text{N/m} \) - Velocity \( v = 4.7 \, \text{m/s} \) **Solution Approach:** 1. Calculate the normal force. 2. Determine the force of kinetic friction. 3. Use Hooke’s Law to find the spring stretch required to overcome friction. The solution involves applying Newton’s laws and understanding the relationship between friction, spring force, and motion. **Note:** This exercise integrates concepts from mechanics, including frictional forces and Elasticity (spring behavior). Solving this problem will enhance your understanding of these principles in practical scenarios.
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