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As shown in the figure below, a 2.25 kg block is released from rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 15.0 cm that has a coefficient of kinetic friction μk = 0.710. Find h (in m) such that the block's speed after crossing the rough patch is 2.80 m/s.

As shown in the figure below, a 2.25 kg block is released from rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 15.0 cm that has a coefficient of kinetic friction μk = 0.710. Find h (in m) such that the block's speed after crossing the rough patch is 2.80 m/s.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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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As shown in the figure below, a 2.25 kg block is released from rest on a ramp of height h.

When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 15.0 cm that has a coefficient of kinetic friction μk = 0.710. Find h (in m) such that the block's speed after crossing the rough patch is 2.80 m/s.
 
_____________ m
### Understanding Motion on a Track with a Rough Patch #### Diagram Explanation The provided diagram illustrates the scenario of a block moving over a track that includes a rough patch. Here is a detailed description: 1. **Initial Position and Velocity:** - A block starts from rest and begins to move to the left (indicated by the green arrow and the symbol \(\vec{v}\)). 2. **Rough Patch:** - As the block moves to the left, it encounters a rough patch on the track. - The rough patch is marked with a wavy line and spans 15.0 cm. - This patch likely introduces friction, affecting the block's motion. 3. **Curved Track and Height (h):** - After covering the rough patch, the block moves up a curved section of the track. - The curved section elevates the block to a height \(h\), where it momentarily comes to rest. - "h" represents the vertical displacement from the lower horizontal section to the top of the curved section. This setup can be used to explore concepts such as kinetic energy, work done by friction, potential energy, and energy conservation principles in physics. ##### Key Elements: - **Block:** The object in motion. - **Green Arrow (\(\vec{v}\)):** Indicates the direction of the block's velocity. - **Rough Patch:** A segment introducing friction, impacting the block’s kinetic energy. - **Curved Track:** Leads the block to a vertical height \(h\). By analyzing the illustrated scenario, students can learn about important physics principles such as: - **Energy Transformation**: Conversion of kinetic energy to potential energy and vice versa. - **Effects of Friction**: How the rough patch reduces the block's kinetic energy due to the work done against frictional forces. - **Kinematics and Dynamics**: Principles governing the block’s motion. This diagram serves as a visual aid for understanding the intricate details and practical applications of energy conservation and the work-energy principle in physics.
Transcribed Image Text:### Understanding Motion on a Track with a Rough Patch #### Diagram Explanation The provided diagram illustrates the scenario of a block moving over a track that includes a rough patch. Here is a detailed description: 1. **Initial Position and Velocity:** - A block starts from rest and begins to move to the left (indicated by the green arrow and the symbol \(\vec{v}\)). 2. **Rough Patch:** - As the block moves to the left, it encounters a rough patch on the track. - The rough patch is marked with a wavy line and spans 15.0 cm. - This patch likely introduces friction, affecting the block's motion. 3. **Curved Track and Height (h):** - After covering the rough patch, the block moves up a curved section of the track. - The curved section elevates the block to a height \(h\), where it momentarily comes to rest. - "h" represents the vertical displacement from the lower horizontal section to the top of the curved section. This setup can be used to explore concepts such as kinetic energy, work done by friction, potential energy, and energy conservation principles in physics. ##### Key Elements: - **Block:** The object in motion. - **Green Arrow (\(\vec{v}\)):** Indicates the direction of the block's velocity. - **Rough Patch:** A segment introducing friction, impacting the block’s kinetic energy. - **Curved Track:** Leads the block to a vertical height \(h\). By analyzing the illustrated scenario, students can learn about important physics principles such as: - **Energy Transformation**: Conversion of kinetic energy to potential energy and vice versa. - **Effects of Friction**: How the rough patch reduces the block's kinetic energy due to the work done against frictional forces. - **Kinematics and Dynamics**: Principles governing the block’s motion. This diagram serves as a visual aid for understanding the intricate details and practical applications of energy conservation and the work-energy principle in physics.
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