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JJBladester
Gold Member
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Homework Statement
A 10kg disk contacts an inclined surface. A 11Nm couple M is applied. The coefficient of friciton is 0.4. Determine the normal force at point D, the angular acceleration [itex]\alpha [/itex], and the force of the rod C.
Answers:
N=115.9 Newtons
[itex]\alpha [/itex]=2.25rad/s2
C=77.19 Newtons
Homework Equations
[tex]\sum F_x=m\bar{a}_x[/tex]
[tex]\sum F_y=m\bar{a}_y[/tex]
[tex]\sum M_G=\bar{I}\alpha[/tex]
[itex]\bar{x}[/itex] and [itex]\bar{y}[/itex] are the coordinates of the mass center (G) of the disk.
The Attempt at a Solution
First, I drew a free-body diagram which you can see if you click the image above.
From the FBD, my first goal is to find the normal force (N) at point D.
I'm having a hard time doing that because I end up with two equations and 3 unknowns.
I don't konw N, C, or a.
[tex]\sum F_x=\mu _kNcos(30)+C-Ncos(30)=macos(30)[/tex]
[tex]N(\mu _k-1)+C=ma[/tex]
[tex]\sum F_y=\mu_kNsin(30)-mg+Nsin(30)=masin(30)[/tex]
[tex]-2N=-mg-C[/tex]
[tex]N=\frac{mg+C}{2}[/tex]
So... I have an expression for N, but it includes another unknown, C (the force of the rod on the disk).
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EDIT:
Figured it out... I needed to set both (ma)'s equal to zero. Also, I did the sin and cos for the frictional force in reverse.
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