A 6.9-kg bowling ball is attached to the end of a nylon (Young's modulus 3.7x10⁹ N/m²) cord with a cross-sectional area of 3.3x10-5 m². The other end of the cord is fixed to the ceiling. When the bowling ball is pulled to one side and released from rest, it swings downward in a circular arc. At the instant it reaches its lowest point, the bowling ball is 1.2 m lower than the point it was released from, and the cord is stretched 3.3x10-³ m from its unstrained length. What is the unstrained length of the cord? Hint: When calculating any quantity other than the strain, ignore the increase in length of the cord. Lo họ họ

A 6.9-kg bowling ball is attached to the end of a nylon (Young's modulus 3.7x10⁹ N/m²) cord with a cross-sectional area of 3.3x10-5 m². The other end of the cord is fixed to the ceiling. When the bowling ball is pulled to one side and released from rest, it swings downward in a circular arc. At the instant it reaches its lowest point, the bowling ball is 1.2 m lower than the point it was released from, and the cord is stretched 3.3x10-³ m from its unstrained length. What is the unstrained length of the cord? Hint: When calculating any quantity other than the strain, ignore the increase in length of the cord. Lo họ họ

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

Mechanical Properties of Solids

There are three types of matter- solid, liquid and gas. Out of them, solids have a rigid shaped and size. The intermolecular forces of attractions in solids are greatest. Mechanical properties are the physical properties of a material which it shows, when it is provided with certain amount of force or load. These properties are to be kept in mind for various purposes. When a force is applied to an object, the object may or may not get deformed depending upon its elastic property. But every time the object develops a restoring force against the force applied. This is commonly known as stress. If the object changes its dimensions due to the force applied it develops strain ( which is the ratio of change in dimension to the original dimension).

Question

A 6.9-kg bowling ball is attached to the end of a nylon (Young's modulus \(3.7 \times 10^9 \, \text{N/m}^2\)) cord with a cross-sectional area of \(3.3 \times 10^{-5} \, \text{m}^2\). The other end of the cord is fixed to the ceiling. When the bowling ball is pulled to one side and released from rest, it swings downward in a circular arc. At the instant it reaches its lowest point, the bowling ball is 1.2 m lower than the point it was released from, and the cord is stretched \(3.3 \times 10^{-3} \, \text{m}\) from its unstrained length. What is the unstrained length of the cord?

**Hint**: When calculating any quantity other than the strain, ignore the increase in length of the cord.

**Diagram Explanation**:
- The diagram shows a cord fixed to the ceiling with a bowling ball attached at the other end.
- The initial position of the ball is shown on the right side of the diagram.
- \(L_0\) is labeled as the unstrained length of the cord.
- A dashed line represents the vertical distance \(h_0 - h_f\), indicating the height difference of 1.2 m when the ball is at the lowest point.
- The velocity \(v_t\) is indicated by an arrow as the ball swings to the left.

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