Solve Dynamics Problem: Find Friction Force at θ=80° & 40°

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SUMMARY

The discussion focuses on calculating the friction force acting on a mass (E) moving along a semicircular plate rotating around the AD axis at a constant speed of 14 rad/s. The coefficients of friction are specified as 0.35 for static and 0.25 for dynamic friction. The primary objective is to determine whether the mass will move for angles θ = 80º and θ = 40º, and to find the magnitude and direction of the friction force at time t0 using Newton's second law and rotational dynamics equations.

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Homework Statement


I drew this to make it easier to understand:
http://img142.imageshack.us/img142/2729/problemagc0.th.jpg
E (mass: 400g) can move along the semicircle.
ABCD is a plate rotating around (AD) axis at constant speed (14 rad/s).
Coefficients of friction are 0.35 (static) and 0.25 (dynamic).
I need to find out whether E will move for θ = 80º and for θ = 40º. Also I need to find the module and direction of the friction force for t0.

Homework Equations


None.

The Attempt at a Solution


I applied Newton's second law.
Σ Fext = mg + N1 + N2 + f
Where:
mg is E's weight
N1 is the normal force in the (ABC) plane
N2 is the normal force perpendicular to the (ABC) plane
f is the friction force
I did this also so that you understand what I mean -just in case... :)
http://img88.imageshack.us/img88/4488/esquemabr8.th.jpg

Then I think I must use:
aE = aO + aE/O + ωx(ωxOE) + αxOE + 2ωxvE/O
With:
α = dω/dt = 0
ω = 14 j
OE = (0.65 - sin(θ)*0.25) iI hope you can help me out here. Thanks a lot!
 
Last edited by a moderator:
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Bump, anyone?
Thanks again.
 
Bump, please give me a hand...
 

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