The accompanying figure shows a frictionless channel in the shape of a segment of a circle with center at "O". The channel has been anchored to a frictionless horizontal tabletop. You are looking down at the table. Forces exerted by the air are negligible. A ball is shot at high speed into the channel at "p" and exits at "r." Which path in the figure below would the ball most closely follow after it exits the channel at "r" and moves across the frictionless tabletop? (B) (C) (D) (E)
The accompanying figure shows a frictionless channel in the shape of a segment of a circle with center at "O". The channel has been anchored to a frictionless horizontal tabletop. You are looking down at the table. Forces exerted by the air are negligible. A ball is shot at high speed into the channel at "p" and exits at "r." Which path in the figure below would the ball most closely follow after it exits the channel at "r" and moves across the frictionless tabletop? (B) (C) (D) (E)
College Physics
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Chapter1: Units, Trigonometry. And Vectors
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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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
Transcribed Image Text:**Title: Understanding Motion Through a Frictionless Channel**
The image presents a frictionless channel shaped like a segment of a circle with its center at "O." This channel is anchored to a frictionless horizontal tabletop, offering an overhead view. In this setup, air resistance is negligible. A ball is introduced at point "p" and exits at point "r."
### Diagram Details:
1. **Circular Segment**: The channel is part of a circle with reference points marked as "p," "q," and "r." The circular motion within dictates how the ball travels in the channel.
2. **Frictionless Environment**: Both the channel and the tabletop are frictionless, meaning the ball maintains its speed unless acted upon by another force.
3. **Ball Trajectory**: Once the ball exits the channel at "r," it will continue in a specific path across the tabletop.
### Path Analysis:
The second part of the image requires choosing the most accurate path the ball will follow after exiting at "r." The options are marked as (A), (B), (C), (D), and (E), all being straight-line paths, due to the conservation of momentum and absence of external forces.
- **Path (B)** is the correct trajectory, as it illustrates the ball continuing in a straight line from "r," following the vector of its exit momentum from the circular channel. This is consistent with Newton's first law of motion, which states that an object in motion will stay in motion at a constant velocity unless acted upon by an external force.
This exercise demonstrates key physics principles, including inertia, momentum, and the effects of a frictionless environment.
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