**Problem Statement:**In the game of tetherball, a rope with length \( l = 1.25\, \text{m} \) connects a ball with mass \( m = 0.550\, \text{kg} \) to the top of a vertical pole so that the ball can spin around the pole as shown in the figure. The tension force in the rope is \( 9.4\, \text{N} \).**Questions:**1. What is the angle the rope makes with the vertical?2. What is the speed \( v \) of the ball as it rotates around the pole?**Visual Description:**The diagram illustrates a vertical pole with a rope attached to its top, extending outward to the tetherball. The length of the rope is \( l = 1.25 \, \text{m} \). The ball is shown spinning around the pole, making an angle \( \theta \) with the vertical line. The tension in the rope (\( T = 9.4 \, \text{N} \)) pulls the ball.The illustration includes:- A vertical pole anchored to a base.- A rope attached to the top of the pole, angled away from the pole.- A ball representing the mass \( m \), connected to the end of the rope.- An indication of the rotational motion with a dotted circular trajectory and an arrow showing the direction of the spin. **Purpose of the Diagram:**The purpose of the visual aid is to help in understanding the physical setup of the problem, which involves parameters such as:- The length of the rope,- The mass of the ball,- The tension in the rope,- The angle the rope makes with the vertical,- The rotational speed of the ball.**Guidelines for the Problem:**To find the angle \( \theta \) that the rope makes with the vertical and the speed \( v \) of the ball, one needs to analyze the forces involved and apply principles from circular motion and trigonometry.---**Educational Benefits:**This problem helps students apply concepts of tension, centripetal force, and circular motion in physics. By solving this, learners enhance their understanding of the mechanics governing rotational systems and the interplay of forces in equilibrium.

Answered: Image /qna-images/answer/9ee7de2c-5dc9-4656-bce5-8e17342ce87e.jpg

4) In the game of tetherball a rope with length =1.25 m connects a ball with mass m=0.550 kg to the top of a vertical pole so that the ball can spin around the pole as shown in the figure. The tension force in the rope is 9.4 N. What is the angle the rope makes with the vertical? What is the speed v of the ball as it rotates around the pole? PH

4) In the game of tetherball a rope with length =1.25 m connects a ball with mass m=0.550 kg to the top of a vertical pole so that the ball can spin around the pole as shown in the figure. The tension force in the rope is 9.4 N. What is the angle the rope makes with the vertical? What is the speed v of the ball as it rotates around the pole? PH

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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Concept explainers

Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

**Problem Statement:**

In the game of tetherball, a rope with length \( l = 1.25\, \text{m} \) connects a ball with mass \( m = 0.550\, \text{kg} \) to the top of a vertical pole so that the ball can spin around the pole as shown in the figure. The tension force in the rope is \( 9.4\, \text{N} \).

**Questions:**
1. What is the angle the rope makes with the vertical?
2. What is the speed \( v \) of the ball as it rotates around the pole?

**Visual Description:**
The diagram illustrates a vertical pole with a rope attached to its top, extending outward to the tetherball. The length of the rope is \( l = 1.25 \, \text{m} \). The ball is shown spinning around the pole, making an angle \( \theta \) with the vertical line. The tension in the rope (\( T = 9.4 \, \text{N} \)) pulls the ball.

The illustration includes:
- A vertical pole anchored to a base.
- A rope attached to the top of the pole, angled away from the pole.
- A ball representing the mass \( m \), connected to the end of the rope.
- An indication of the rotational motion with a dotted circular trajectory and an arrow showing the direction of the spin.

**Purpose of the Diagram:**
The purpose of the visual aid is to help in understanding the physical setup of the problem, which involves parameters such as:
- The length of the rope,
- The mass of the ball,
- The tension in the rope,
- The angle the rope makes with the vertical,
- The rotational speed of the ball.

**Guidelines for the Problem:**

To find the angle \( \theta \) that the rope makes with the vertical and the speed \( v \) of the ball, one needs to analyze the forces involved and apply principles from circular motion and trigonometry.

---

**Educational Benefits:**
This problem helps students apply concepts of tension, centripetal force, and circular motion in physics. By solving this, learners enhance their understanding of the mechanics governing rotational systems and the interplay of forces in equilibrium.

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