A solid uniform ball with massm 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. L

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Chapter1: Units, Trigonometry. And Vectors
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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.

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

Problem
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.
L
d
r
m
Transcribed Image Text:Problem 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. L d r m
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
ΣFΤ
= 0
Simplifying this results to
T =
g/
(4)
Analyzing the figure above, we arrive at
(4) = sqrt(
+
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
Transcribed Image Text: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 ΣFΤ = 0 Simplifying this results to T = g/ (4) Analyzing the figure above, we arrive at (4) = sqrt( + 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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