Can I use U_k for the friction coefficient or do I need to use U_k while its moving and U_s for the instant when it changes direction?
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Fall 2008 -- Purdue University -- West Lafayette, IN
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8 comments:
Rolling without slipping means that the friction force between the wheel and ground is less than mu_s*N. Set up and solve the problem assuming no slip (friction force is simply a reaction). To find the maximum x0, then set f = mu_s*N.
mu_k is NOT used in this problem.
Can we leave our final answer in terms of the acceleration in the x direction, or should we solve for the acceleration in terms of another variable?
I have found my x(t), xdot(t), and xdot_dot(t), but I do not understand how you use these equations to solve for the impending mu of the friction. When I simply plug them in for xdot_dot and x in my sum forces X equation I end up with mu=0. So I know I can't plug straight in, so then what other equations would I use in order to find the mu max?
Then I believe once I have the mu max, I then plug my x and xdot_dot in to my sum forces x, with my new mu, and then solve for Xo?
Mark
I don't see how I would use mu either. I determined the friction force by solving for the moment about G. Does using mu_s just provide an alternate method to find the solution?
I'm stuck at the same spot. I have two equations for F: mu_s*m*g and one from the sum of moments equation. Plugging x, x_dot, and x_dot_dot into my EOM hasn't worked. I'm wondering why I can't set my two equations for F equal to each other and solve for x_0 that way?
-John
A way that might work would be to solve for theta_double_dot from the kinematics so that way we would have an x_double_dot that we could also get from differentiating the solution. Use that in the moment equation so we would have our friction force and the x_0 and just solve for the x_0that the question asks for. It would still be all symbolically though and in terms of mu_s if we sub it in for the friction force, so I don't really see either how solving for mu_s helps.
When I solved the problem, I solved for x_0 in terms of mu_s, and just left mu_s as a constant variable (similar to m, r) in the solution. Is this not correct? I also attempted to solve the differential equation by assuming a solution of the form x = Acos(omega_n*t) + Bsin(omega_n*t) but didn't think this would get me anywhere, since I was not looking for x_0 as a function of time.
The friction force depends on the response x(t). You need to find x(t) by solving the differential equation of motion for the disk. See the recent post that outlines the steps for this.
Let us know if you have questions.
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