Two balls are tied together via string and then swung in a vertical circular path using a second string, as shown in the figure. During this motion, the two strings are co-linear at all times. The first ball has mass m1 = 0.4 kg, and the second has m2 = 0.2 kg. Each of the two strings has an individual length l = 36 cm. At the top of its swing, m2 is traveling at v = 3.0 m/s. (a) What is the tension in String 1 at this instant? (b) What is the tension in String 2 at this instant? (c) Which string will break first if the combination is rotated faster and faster? (i.e. which tension will grow too large?) String 1 e String 2

Two balls are tied together via string and then swung in a vertical circular path using a second string, as shown in the figure. During this motion, the two strings are co-linear at all times. The first ball has mass m1 = 0.4 kg, and the second has m2 = 0.2 kg. Each of the two strings has an individual length l = 36 cm. At the top of its swing, m2 is traveling at v = 3.0 m/s. (a) What is the tension in String 1 at this instant? (b) What is the tension in String 2 at this instant? (c) Which string will break first if the combination is rotated faster and faster? (i.e. which tension will grow too large?) String 1 e String 2

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

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

**Problem Statement:**

Two balls are tied together via a string and then swung in a vertical circular path using a second string, as shown in the figure. During this motion, the two strings are co-linear at all times. The first ball has a mass \( m_1 = 0.4 \, \text{kg} \), and the second has \( m_2 = 0.2 \, \text{kg} \). Each of the two strings has an individual length \( \ell = 36 \, \text{cm} \). At the top of its swing, \( m_2 \) is traveling at \( v = 3.0 \, \text{m/s} \).

**Questions:**
(a) What is the tension in String 1 at this instant?
(b) What is the tension in String 2 at this instant?
(c) Which string will break first if the combination is rotated faster and faster? (i.e., which tension will grow too large?)

**Diagram Explanation:**

The diagram shows two balls connected by strings and swinging in a circular motion. The setup includes:

- Two masses, \( m_1 \) and \( m_2 \):
- \( m_1 \) is positioned above \( m_2 \).
- \( m_1 \) is connected to the pivot point by String 1.
- \( m_2 \) is connected to \( m_1 \) by String 2.

- Both strings have a length \( \ell \).
- At the top of the circular path, \( m_2 \) moves with velocity \( v \).

- The arrows indicate the direction of velocity and tension.

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