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A 3.00-kg block is placed at the top of a track consisting of two frictionless quarter circles of radius ?=3.00 m connected by a 5.00-m-long, straight, horizontal surface as shown in the figure. The coefficient of kinetic friction between the block and the horizontal surface is ?k=0.100. The block is released from rest. What maximum vertical height ? does the block reach on the right‑hand section of the track? y = ? (in m)

A 3.00-kg block is placed at the top of a track consisting of two frictionless quarter circles of radius ?=3.00 m connected by a 5.00-m-long, straight, horizontal surface as shown in the figure. The coefficient of kinetic friction between the block and the horizontal surface is ?k=0.100. The block is released from rest. What maximum vertical height ? does the block reach on the right‑hand section of the track? y = ? (in m)

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A 3.00-kg block is placed at the top of a track consisting of two frictionless quarter circles of radius ?=3.00 m connected by a 5.00-m-long, straight, horizontal surface as shown in the figure. The coefficient of kinetic friction between the block and the horizontal surface is ?k=0.100. The block is released from rest.

What maximum vertical height ? does the block reach on the right‑hand section of the track?

y = ? (in m)
**Diagram Explanation for Educational Website** The image depicts a classic physics problem involving forces and motion on a curved surface, specifically the motion of a block on a curved track. ### Key Components: 1. **Block (Pink Square)** - Positioned at the top left of the track. - Represents an object that will move under the influence of gravity. 2. **Curved Track (Green)** - Starts with a steep curve where the block is placed, then transitions into a straight horizontal section and ends with another curve at the right, mirroring the initial curve. - The curvature helps demonstrate how potential energy is converted into kinetic energy as the block moves down the track. 3. **Arrow (Black)** - Positioned on the right descending section of the track. - Indicates the direction of motion as the block moves down the slope under the influence of gravity. ### Conceptual Focus: - **Potential Energy to Kinetic Energy Conversion:** The block starts with maximum potential energy at the top of the track, which transforms into kinetic energy as it moves downward. - **Motion and Forces:** The diagram visually represents forces acting on the block, particularly gravity, which causes it to accelerate down the curved path. - **Energy Conservation:** The closed curve demonstrates the principle of energy conservation, assuming no friction, the mechanical energy at the top equals the mechanical energy at any other point on the track. This diagram is crucial for understanding basic physics principles such as energy transformation, motion, and the effects of gravity on an object in a curved path.
Transcribed Image Text:**Diagram Explanation for Educational Website** The image depicts a classic physics problem involving forces and motion on a curved surface, specifically the motion of a block on a curved track. ### Key Components: 1. **Block (Pink Square)** - Positioned at the top left of the track. - Represents an object that will move under the influence of gravity. 2. **Curved Track (Green)** - Starts with a steep curve where the block is placed, then transitions into a straight horizontal section and ends with another curve at the right, mirroring the initial curve. - The curvature helps demonstrate how potential energy is converted into kinetic energy as the block moves down the track. 3. **Arrow (Black)** - Positioned on the right descending section of the track. - Indicates the direction of motion as the block moves down the slope under the influence of gravity. ### Conceptual Focus: - **Potential Energy to Kinetic Energy Conversion:** The block starts with maximum potential energy at the top of the track, which transforms into kinetic energy as it moves downward. - **Motion and Forces:** The diagram visually represents forces acting on the block, particularly gravity, which causes it to accelerate down the curved path. - **Energy Conservation:** The closed curve demonstrates the principle of energy conservation, assuming no friction, the mechanical energy at the top equals the mechanical energy at any other point on the track. This diagram is crucial for understanding basic physics principles such as energy transformation, motion, and the effects of gravity on an object in a curved path.
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