Answered: A solid uniform ball with mass m and…

A solid uniform ball with mass m and diameter d is supported against a vertical frictionless wall by a thin massless wire of length L. a) Find the tension in the wire.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 40PQ: A brass wire and a steel wire, both of the same length, are extended by 1.0 mm under the same force....

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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 solid uniform ball with mass m and diameter d is supported against a vertical frictionless wall by a thin massless wire of length L. a) Find the tension in the wire.

Solution

Let us first derive the expression for the tension.

By Newton's First Law

ΣF = ___

the components of force that makes this so is

ΣF = T___ - ___ = 0

Simplifying this results to

T = ___g/___(ϕ)

Analyzing the figure above, we arrive at

___(ϕ) = sqrt(___² + ___ ) / ( ___/___ + ___ )

By substitution, we arrive at the following:

T = ___ ( ___ + 2___ ) g / ( ___sqrt ( ___² + ___ ) )

If the ball has a mass of 45 kg and diameter 32 cm, while the wire has a length of 30 cm. The tension is equal to

T = ___0.370 N

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