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= = A block of mass m 2 kg moves with an initial velocity vo 5 m/s across a surface with a coefficient of kinetic friction µ = 0.2. The mass approaches a spring with spring constant k = 20 N/m.

= = A block of mass m 2 kg moves with an initial velocity vo 5 m/s across a surface with a coefficient of kinetic friction µ = 0.2. The mass approaches a spring with spring constant k = 20 N/m.

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**Title: Conservation of Energy with Spring Compression and Friction** **Problem Statement:** A block of mass \( m = 2 \, \text{kg} \) moves with an initial velocity \( v_0 = 5 \, \text{m/s} \) across a surface with a coefficient of kinetic friction \( \mu_k = 0.2 \). The mass approaches a spring with a spring constant \( k = 20 \, \text{N/m} \). **Diagram Explanation:** The diagram illustrates the following: - A block of mass \( m \) is moving towards a spring. - The spring is positioned at the left end of the surface. - The surface has two friction coefficients indicated: kinetic (\( \mu_k = 0.2 \)) and static (\( \mu_s \)) friction, acting over the entire length. - The initial velocity \( v_0 \) of the block is directed towards the spring. - The distance \( d = 5 \, \text{m} \) is marked from the block's starting position to the spring's equilibrium position. **Questions:** (a) What is the maximum compression \( x \) that the spring experiences if the block is a distance \( d = 5 \, \text{m} \) away from the spring’s equilibrium position when it has velocity \( v_0 \)? Use energy conservation. (b) If \( \mu_s = 0.3 \), will the block remain at rest upon compressing the spring? If so, what are the magnitude and direction of the force of friction acting on the block at this point? If not, how far does the block travel before stopping upon rebounding from the spring? *(If answering this last question, you will find it helpful to review PS-05, problem 6!)* **Note:** Use principles of energy conservation to address part (a) and analyze forces for part (b).
Transcribed Image Text:**Title: Conservation of Energy with Spring Compression and Friction** **Problem Statement:** A block of mass \( m = 2 \, \text{kg} \) moves with an initial velocity \( v_0 = 5 \, \text{m/s} \) across a surface with a coefficient of kinetic friction \( \mu_k = 0.2 \). The mass approaches a spring with a spring constant \( k = 20 \, \text{N/m} \). **Diagram Explanation:** The diagram illustrates the following: - A block of mass \( m \) is moving towards a spring. - The spring is positioned at the left end of the surface. - The surface has two friction coefficients indicated: kinetic (\( \mu_k = 0.2 \)) and static (\( \mu_s \)) friction, acting over the entire length. - The initial velocity \( v_0 \) of the block is directed towards the spring. - The distance \( d = 5 \, \text{m} \) is marked from the block's starting position to the spring's equilibrium position. **Questions:** (a) What is the maximum compression \( x \) that the spring experiences if the block is a distance \( d = 5 \, \text{m} \) away from the spring’s equilibrium position when it has velocity \( v_0 \)? Use energy conservation. (b) If \( \mu_s = 0.3 \), will the block remain at rest upon compressing the spring? If so, what are the magnitude and direction of the force of friction acting on the block at this point? If not, how far does the block travel before stopping upon rebounding from the spring? *(If answering this last question, you will find it helpful to review PS-05, problem 6!)* **Note:** Use principles of energy conservation to address part (a) and analyze forces for part (b).
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