A pendulum is constructed by attaching a small metal ball to one end of a string of length \( L = 1.45 \, \text{m} \) that hangs from the ceiling, as shown in the figure. The ball is released when it is raised high enough for the string to make an angle of \( \theta = 20.0^\circ \) with the vertical. **Diagram Explanation:** The diagram shows a pendulum setup: - A string of length \( L \) is attached to a ceiling. - A ball hangs from the string, forming an angle \( \theta \) with the vertical line. - The angle is labeled as \( \theta \) and the length of the string as \( L \). - The ball is shown at two positions: one at the top when released, and another at the bottom of its swing with a horizontal velocity \( v = ? \). **Question:** With what speed \( v \) is the ball moving at the bottom of its swing? \[ v = \, \boxed{} \, \text{m/s} \] **Multiple-Choice Question:** Does the mass of the ball affect the answer? - \( \bigcirc \) Yes, because the work done on the ball by the gravitational force depends on the mass. - \( \bigcirc \) No, because the ball’s speed is independent of its mass. - \( \bigcirc \) No, because the change in string tension counteracts the change in mass. - \( \bigcirc \) Yes, because changing the mass changes the ball's inertia.
A pendulum is constructed by attaching a small metal ball to one end of a string of length \( L = 1.45 \, \text{m} \) that hangs from the ceiling, as shown in the figure. The ball is released when it is raised high enough for the string to make an angle of \( \theta = 20.0^\circ \) with the vertical. **Diagram Explanation:** The diagram shows a pendulum setup: - A string of length \( L \) is attached to a ceiling. - A ball hangs from the string, forming an angle \( \theta \) with the vertical line. - The angle is labeled as \( \theta \) and the length of the string as \( L \). - The ball is shown at two positions: one at the top when released, and another at the bottom of its swing with a horizontal velocity \( v = ? \). **Question:** With what speed \( v \) is the ball moving at the bottom of its swing? \[ v = \, \boxed{} \, \text{m/s} \] **Multiple-Choice Question:** Does the mass of the ball affect the answer? - \( \bigcirc \) Yes, because the work done on the ball by the gravitational force depends on the mass. - \( \bigcirc \) No, because the ball’s speed is independent of its mass. - \( \bigcirc \) No, because the change in string tension counteracts the change in mass. - \( \bigcirc \) Yes, because changing the mass changes the ball's inertia.
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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![A pendulum is constructed by attaching a small metal ball to one end of a string of length \( L = 1.45 \, \text{m} \) that hangs from the ceiling, as shown in the figure. The ball is released when it is raised high enough for the string to make an angle of \( \theta = 20.0^\circ \) with the vertical.
**Diagram Explanation:**
The diagram shows a pendulum setup:
- A string of length \( L \) is attached to a ceiling.
- A ball hangs from the string, forming an angle \( \theta \) with the vertical line.
- The angle is labeled as \( \theta \) and the length of the string as \( L \).
- The ball is shown at two positions: one at the top when released, and another at the bottom of its swing with a horizontal velocity \( v = ? \).
**Question:**
With what speed \( v \) is the ball moving at the bottom of its swing?
\[ v = \, \boxed{} \, \text{m/s} \]
**Multiple-Choice Question:**
Does the mass of the ball affect the answer?
- \( \bigcirc \) Yes, because the work done on the ball by the gravitational force depends on the mass.
- \( \bigcirc \) No, because the ball’s speed is independent of its mass.
- \( \bigcirc \) No, because the change in string tension counteracts the change in mass.
- \( \bigcirc \) Yes, because changing the mass changes the ball's inertia.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe799f64b-1f0b-4ff1-9ee3-5090ddf07729%2F6052f504-4337-411a-966f-bdb2ff42de70%2F5tthx0g_processed.png&w=3840&q=75)
Transcribed Image Text:A pendulum is constructed by attaching a small metal ball to one end of a string of length \( L = 1.45 \, \text{m} \) that hangs from the ceiling, as shown in the figure. The ball is released when it is raised high enough for the string to make an angle of \( \theta = 20.0^\circ \) with the vertical.
**Diagram Explanation:**
The diagram shows a pendulum setup:
- A string of length \( L \) is attached to a ceiling.
- A ball hangs from the string, forming an angle \( \theta \) with the vertical line.
- The angle is labeled as \( \theta \) and the length of the string as \( L \).
- The ball is shown at two positions: one at the top when released, and another at the bottom of its swing with a horizontal velocity \( v = ? \).
**Question:**
With what speed \( v \) is the ball moving at the bottom of its swing?
\[ v = \, \boxed{} \, \text{m/s} \]
**Multiple-Choice Question:**
Does the mass of the ball affect the answer?
- \( \bigcirc \) Yes, because the work done on the ball by the gravitational force depends on the mass.
- \( \bigcirc \) No, because the ball’s speed is independent of its mass.
- \( \bigcirc \) No, because the change in string tension counteracts the change in mass.
- \( \bigcirc \) Yes, because changing the mass changes the ball's inertia.
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