Calculating Tension in a Revolving Mass: Homework Solution

[sunnnystrong]

Homework Statement

The figure shows two wires that are tied to a 970g mass which revolves in a horizontal circle at a constant 7.5 m/s. What is the tension in the upper wire?

The wires are both 1m long, and are attached to a pole. The radius is cos(30 degrees). It's an equilateral triangle.

Homework Equations

∑F = m*a

The Attempt at a Solution

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∑Fy = 0.
∑Fx = (m*v^2) / r

First I looked at the forces in the y-direction. Down = negative.
The upper rope = T1. The lower rope = T2.

(.5)T1 - (.5)T2 - mg = 0
*Solve for T1*
T2 + 2*m*g = T1 // EQN 1

Next, in the X-Direction. Inward = positive.

T1cos(30) + T2cos(30) = (m*v^2)/r
Plug in value for T1 to solve for T2.
2*T2*cos(30) + 2*m*g*cos(30) = (m*v^2)/r
[(m*v^2)/r - 2*m*g*cos(30) ] / (2cos(30) = T2
T2 = 26.868 N

Plug into EQN 1 and I got T1 = 46 N

 

[gneill]

Looks good.

 

[sunnnystrong]

Looks good.

Thank you!