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This problem involves a block sliding down an inclined plane, looping around a circular path, and then compressing a spring. Here’s a breakdown of how to solve each part:

### Part a: Calculating Maximum Compression of the Spring
1. **Energy Conservation**:
   - Initially, the block has gravitational potential energy at height \( h = 2.5 \, \text{m} \).
   - As it slides, friction dissipates some energy on the inclined plane and the horizontal surface \( BG \).
   - After the loop, any remaining kinetic energy is used to compress the spring.

2. **Calculating Initial Potential Energy**:
   \[
   PE = mgh = 0.6 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 2.5 \, \text{m}
   \]

3. **Frictional Work Done**:
   - **On Incline (AB)**:
     Use the coefficient of kinetic friction \( \mu = 0.3 \) along distance \( AB \).
   - **On Horizontal Surface (BG)**:
     Similarly, calculate work done by friction along \( BG = 0.6 \, \text{m} \).

4. **Loop Dynamics**:
   - For the block to complete the loop, the centripetal force at the top of the loop should be considered.

5. **Spring Compression**:
   - After frictional losses, use energy conservation to find the compression \( x \) of the spring where:
     \[
     \frac{1}{2}kx^2 = \text{Remaining Kinetic Energy}
     \]

### Part b: Normal Force at Position D
1. **Centripetal Force Requirement**:
   At point \( D \), calculate the normal force using centripetal acceleration requirements due to the loop’s radius \( r = 0.5 \, \text{m} \).

Would you like detailed step-by-step calculations for each section? Here are some further questions for exploration:

1. How would the maximum compression change if the spring constant was different?
2. What effect would doubling the mass of the block have on the loop completion?
3. How would a change in the loop’s radius affect the required velocity to complete it?
4. How does the angle of the incline influence the frictional work done?
5. What would happen if friction were present in the loop?

**Tip:** In energy problems with friction, always account for each segment's work done separately.

Un bloque de 0.6 kg se suelta en la posición A, desliza a lo largo del plano inclinado de 45° de inclinación hasta B. A continuación describe el bucle BCDEB, desliza a lo largo del plano horizontal BF y finalmente comprime un muelle de constante k=500 N/m cuyo extremo libre dista 60 cm de B. a. Calcular la máxima deformación del muelle, sabiendo que la altura h de A es de 2.5 m, el radio del bucle r = 0.5 m, y el coeficiente dinámico de rozamiento en el plano horizontal BG y en el inclinado AB es de 0.3. Suponer que no hay rozamiento en el bucle. b. Hallar la fuerza normal en la posición D.

Analyze a physics problem involving a block sliding down an incline, looping through a circular path, and compressing a spring. This problem covers key concepts such as energy conservation, work done by friction, and circular motion. Suitable for high school students (Grades 10-12).

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