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.
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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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
a)
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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