Problem 8.63 Two wires are tied to the 200 g sphere shown in figure. The sphere

Question

Problem 8.63

Two wires are tied to the 200 g sphere shown in figure. The sphere revolves in a horiIzontal circle at a constant speed of 6.80 m/s.

Part A

What is the tension in the upper wire?

Part B

What is the tension in the lower wire?

Part A Two wires are tied to the 200 g sphere shown in figure. The sphere revolves in a horilzontal circle at a constant speed of 6.80 m/s. Figure 1) What is the tension in the upper wire? Express your answer with the appropriate units. Value Units Figure 1 Submit My Answers Give Up Part B What is the tension in the lower wire? Express your answer with the appropriate units. 0.5 m 0.5 m im alueUnits Submit My Answers Give Up

Explanation / Answer

Let the tension in the top wire be T1
Let the tension in the bottom wire be T2

from figure: angle = sin-1(0.5/1) = 30o

Then T1 cos 30 + T2 cos 30 = mv^2/r --->1
and T1 sin 30 = mg + T2 sin 30 ----->2

r = 1 cos 30 = cos30 =>
3T1 + 3T2 = 4mv^2
T1 - T2 = 2mg

=> 6T1 = 6mg+4mv^2 => T1 = mg +(2mv^2)/3
and T2 = (2mv^2)/3 - mg
=> T1 = 8.12 N
and T2 = 4.20 N

Answer :
Tension in Top wire = 8.12 N , Bottom wire = 4.20 N

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