The image depicts a half-pipe with a ball, illustrating a physics problem. ### Diagram Description - **Half-Pipe:** A U-shaped track with two sides labeled: "No-slip" (left side) and "Frictionless" (right side). - **Ball:** Shown at three positions: at the top of the no-slip side, moving down the track, and near the bottom. The ball is solid with a radius of 4.0 cm and a mass of 0.14 kg. ### Problem Statement - **Scenario:** The ball starts from rest at a height of 0.77 m above the bottom on the no-slip side of the half-pipe. As it descends and ascends the frictionless side, we need to find: 1. The angular speed on the frictionless side. 2. The maximum height reached on the frictionless side. ### Instructions 1. **Draw a Pictorial Representation:** Create a diagram similar to the one provided. 2. **List Given Information:** - Radius of the ball: 4.0 cm - Mass of the ball: 0.14 kg - Initial height: 0.77 m 3. **Constraints to Motion:** - No-slip side: Sufficient static friction, so no sliding. - Frictionless side: No friction affecting motion. 4. **Physics Laws:** Use principles of energy conservation and dynamics of rotational motion. 5. **Solve for Angular Velocity:** Calculate angular speed when the ball is on the frictionless side. 6. **Solve for Maximum Height:** Determine how high the ball rises on the frictionless side.

The image depicts a half-pipe with a ball, illustrating a physics problem. ### Diagram Description - Half-Pipe: A U-shaped track with two sides labeled: "No-slip" (left side) and "Frictionless" (right side). - Ball: Shown at three positions: at the top of the no-slip side, moving down the track, and near the bottom. The ball is solid with a radius of 4.0 cm and a mass of 0.14 kg. ### Problem Statement - Scenario: The ball starts from rest at a height of 0.77 m above the bottom on the no-slip side of the half-pipe. As it descends and ascends the frictionless side, we need to find: 1. The angular speed on the frictionless side. 2. The maximum height reached on the frictionless side. ### Instructions 1. Draw a Pictorial Representation: Create a diagram similar to the one provided. 2. List Given Information: - Radius of the ball: 4.0 cm - Mass of the ball: 0.14 kg - Initial height: 0.77 m 3. Constraints to Motion: - No-slip side: Sufficient static friction, so no sliding. - Frictionless side: No friction affecting motion. 4. Physics Laws: Use principles of energy conservation and dynamics of rotational motion. 5. Solve for Angular Velocity: Calculate angular speed when the ball is on the frictionless side. 6. Solve for Maximum Height: Determine how high the ball rises on the frictionless side.

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