- #1
Radarithm
Gold Member
- 158
- 2
Homework Statement
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].
Homework Equations
[itex]ma=mr\omega^2=ml\omega^2\sin{\varphi}[/itex]
Where phi is 45 degrees.
The Attempt at a Solution
Image: http://gyazo.com/8626cda317d6dca7dc1bbe751b643247
FBD: http://postimg.org/image/tez986p19/
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?
Last edited: