# K&K Question 3.5 – Mass and Axle

**1. The problem statement, all variables and given/known data**

A mass *m* is connected to a vertical revolving axle by two strings of length *l*, each making an angle of 45 degrees with the axle, as shown. Both the axle and mass are revolving with constant angular velocity *ω*. Gravity is directed downward.

(a) Draw a clear force diagram for *m*

(b) Find the tension in the upper string, [itex]T_{up}[/itex] and the tension in the lower string, [itex]T_{low}[/itex].

**2. Relevant equations**

[itex]ma=mr\omega^2=ml\omega^2\sin{\varphi}[/itex]

Where phi is 45 degrees.

**3. The attempt at a solution**

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The equations for the x and y directions, respectively:

[itex]T_u\sin{\varphi}-T_d\sin{\varphi}=ml\omega^2\sin{\varphi}[/itex]

[itex]T_u\cos{\varphi}-mg-T_d\cos{\varphi}=ml\omega^2\sin{\varphi}[/itex]

Solving for the tension in the upper cord, I get this:

[itex]T_u=-mg[/itex]

Assuming that the tangent of 45 is 1. Am I on the right track or am I making a mistake right now? If it has to do with reference frames, I wouldn’t know what to do; I know that:

[itex]F_{apparent}=F_{true}+F_{fictitious}[/itex]

I don’t know how to apply it though. Should I continue solving for the tension in the lower rope, or do I need to correct something?

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