(a) the velocity of the block at B, (b) work done by friction as the block slides from B to C, (c) the velocity of the block at C, and

College Physics
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The problem involves a track with three sections: A-B, B-C, and C-D. Here's a detailed breakdown:

1. **Track Description:**
   - **Section A-B:** This is a quarter circle with a radius of 1.5 meters and is frictionless.
   - **Section B-C:** A horizontal span with friction; the coefficient of kinetic friction \( \mu_k \) is 0.3. The length of this span is 3 meters.
   - **Section C-D:** This section is frictionless and contains a spring.

2. **Initial Conditions:**
   - A block with a mass of 1 kg is released from rest at point A.

3. **Observation:**
   - The block compresses the spring by 0.15 meters after sliding on the track.

4. **Tasks:**
   - Determine the following:
     - (a) The velocity of the block at point B.
     - (b) The work done by friction as the block slides from B to C.
     - (c) The velocity of the block at point C.
     - (d) The spring constant of the spring.

5. **Diagram Description:**
   - The diagram shows the track starting at A, curving down to B (quarter circle, frictionless), then following a straight line from B to C (friction  \( \mu_k = 0.3 \)), and finally reaching D where the spring is located.

This problem requires understanding concepts of energy conservation, frictional work, kinematics, and spring compression to solve the given tasks.
Transcribed Image Text:The problem involves a track with three sections: A-B, B-C, and C-D. Here's a detailed breakdown: 1. **Track Description:** - **Section A-B:** This is a quarter circle with a radius of 1.5 meters and is frictionless. - **Section B-C:** A horizontal span with friction; the coefficient of kinetic friction \( \mu_k \) is 0.3. The length of this span is 3 meters. - **Section C-D:** This section is frictionless and contains a spring. 2. **Initial Conditions:** - A block with a mass of 1 kg is released from rest at point A. 3. **Observation:** - The block compresses the spring by 0.15 meters after sliding on the track. 4. **Tasks:** - Determine the following: - (a) The velocity of the block at point B. - (b) The work done by friction as the block slides from B to C. - (c) The velocity of the block at point C. - (d) The spring constant of the spring. 5. **Diagram Description:** - The diagram shows the track starting at A, curving down to B (quarter circle, frictionless), then following a straight line from B to C (friction \( \mu_k = 0.3 \)), and finally reaching D where the spring is located. This problem requires understanding concepts of energy conservation, frictional work, kinematics, and spring compression to solve the given tasks.
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