OM The coefficient of friction is given by μ = 0.100. How far has the spring compressed by the time the block first momentarily comes to rest?

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**Physics Problem: Spring and Friction**

A block of mass \( m = 2.15 \, \text{kg} \) slides along a horizontal table with an initial speed of \( v_0 = 1.00 \, \text{m/s} \). At \( x = 0 \), it collides with a spring that has a spring constant of \( k = 73.00 \, \text{N/m} \). As the block moves, it begins to experience a frictional force.

The coefficient of friction between the block and the table is \( \mu = 0.100 \). The problem is to determine how far the spring will be compressed when the block first comes momentarily to rest.

**Diagram Explanation:**

1. **Initial Scenario**:
   - A block is shown moving horizontally towards a spring with an initial velocity \( v_0 \) depicted by an arrow.
   - The motion occurs on a flat horizontal surface.

2. **Final Scenario**:
   - The block has compressed the spring by a distance \( \Delta x \).
   - The diagram indicates that at this point, the block momentarily comes to rest.

**Question**: How far is the spring compressed, \(\Delta x\), when the block first momentarily stops?

\[ \Delta x = \, \,\, \text{m} \] 

Please fill in the box with the calculation result for \(\Delta x\).
Transcribed Image Text:**Physics Problem: Spring and Friction** A block of mass \( m = 2.15 \, \text{kg} \) slides along a horizontal table with an initial speed of \( v_0 = 1.00 \, \text{m/s} \). At \( x = 0 \), it collides with a spring that has a spring constant of \( k = 73.00 \, \text{N/m} \). As the block moves, it begins to experience a frictional force. The coefficient of friction between the block and the table is \( \mu = 0.100 \). The problem is to determine how far the spring will be compressed when the block first comes momentarily to rest. **Diagram Explanation:** 1. **Initial Scenario**: - A block is shown moving horizontally towards a spring with an initial velocity \( v_0 \) depicted by an arrow. - The motion occurs on a flat horizontal surface. 2. **Final Scenario**: - The block has compressed the spring by a distance \( \Delta x \). - The diagram indicates that at this point, the block momentarily comes to rest. **Question**: How far is the spring compressed, \(\Delta x\), when the block first momentarily stops? \[ \Delta x = \, \,\, \text{m} \] Please fill in the box with the calculation result for \(\Delta x\).
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