A bug slides back and forth in a bowl 15 cm deep, starting from rest at the top, as shown below. The bowl is frictionless except for a 1.4-cm-wide sticky patch on its flat bottom, where the coefficient of kinetic friction is 0.89. How many times does the bug completely cross the sticky region? 15 cm 1.4 cm

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Title: Physics of Motion in a Frictional Environment

### Problem Statement:

A bug slides back and forth in a bowl that is 15 cm deep, starting from rest at the top. The bowl is frictionless except for a 1.4-cm-wide sticky patch on its flat bottom, where the coefficient of kinetic friction is 0.89. The objective is to determine how many times the bug completely crosses the sticky region.

### Diagram Explanation:

The diagram illustrates a cross-sectional view of a bowl shaped in a concave curve. The following details are depicted:

- **Depth of the Bowl**: The maximum depth from the top of the bowl to its base is marked as 15 cm.
- **Sticky Region**: At the flat bottom, there is a sticky region labeled with a width of 1.4 cm. This is where friction is present.
- **Bug**: The bug is shown starting its descent from one of the edges.

### Key Concepts:

- **Frictionless Motion**: Except for the sticky patch, the rest of the bowl allows motion without resistance.
- **Kinetic Friction**: This is present only in the sticky patch, affecting the bug’s motion each time it crosses.

### Learning Objectives:

- To understand the effect of kinetic friction on motion.
- To calculate the distance traveled before the motion ceases.
- To analyze energy conservation and energy dissipation due to friction.

Understanding these principles aids in comprehending how objects move under different conditions and interact with surfaces having varying frictional properties.
Transcribed Image Text:Title: Physics of Motion in a Frictional Environment ### Problem Statement: A bug slides back and forth in a bowl that is 15 cm deep, starting from rest at the top. The bowl is frictionless except for a 1.4-cm-wide sticky patch on its flat bottom, where the coefficient of kinetic friction is 0.89. The objective is to determine how many times the bug completely crosses the sticky region. ### Diagram Explanation: The diagram illustrates a cross-sectional view of a bowl shaped in a concave curve. The following details are depicted: - **Depth of the Bowl**: The maximum depth from the top of the bowl to its base is marked as 15 cm. - **Sticky Region**: At the flat bottom, there is a sticky region labeled with a width of 1.4 cm. This is where friction is present. - **Bug**: The bug is shown starting its descent from one of the edges. ### Key Concepts: - **Frictionless Motion**: Except for the sticky patch, the rest of the bowl allows motion without resistance. - **Kinetic Friction**: This is present only in the sticky patch, affecting the bug’s motion each time it crosses. ### Learning Objectives: - To understand the effect of kinetic friction on motion. - To calculate the distance traveled before the motion ceases. - To analyze energy conservation and energy dissipation due to friction. Understanding these principles aids in comprehending how objects move under different conditions and interact with surfaces having varying frictional properties.
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