So I'm trying to solve this problem and I have reworked it multiple times and I keep getting an answer of 2.86 rad/s, when the answers provided in class say it should be 2.73 rad/s. I don't have any idea what I'm doing wrong but I consistently get 2.86 as my answer. Is it possible the answer given is wrong or am I making some stupid mistake? If it helps, I am getting to a solution where -m*r(thetadot)^2 = -N*sin(theta) + f*cos(theta) and solving for thetadot. This looked good to me, don't know what's wrong with it though..
15 comments:
I am getting exactly the same answer as you (2.86 rad/sec). I am even doing the problem in a slightly different way than you outlined. It leads me to believe the answer given is wrong... but I hate to say that, especially when Dr. Krousgrill will most likely point out our error haha.
Actually, i'm getting the same answer again and again. You set the value of f to be fmax-Wsin30 right? I'm not so sure but the anwer given might be wrong or i'm making the same mistake that you guys are.
rhardist:
You equation is close but the sign in front of two of your terms is incorrect. The equation I used is:
N*sin(theta)-f*cos(theta)=-m*r(thetadot)^2
I got the answer listed on the solutions sheet using this equation.
Hmm.. I was excited at first to try that solution, and then I realized I get the same answer. I had my r vector drawn to the right which technically isn't a good idea, but that is why my signs were switched, but switching the sign in front of N and f doesn't actually change the magnitude of the left side of the equation, only the overall sign, which leaves me back at my original question :(
If we have the same equation for the er direction what is your equation in the k direction? That might be where the error is.
I agree with rhardist, switching the signs on the terms that Emily specified will not change your answer. Also, how would the equation in the k direction change anything? I computed the same answer as rhardist in a different manner, neglecting completely any summation of forces in the k. Is it necessary to sum in the k, or am i just getting lucky on this problem (and on the amusement ride problem from the last hw)?
If you don't have an equation in the k direction how are you solving for the normal force?
I see what you mean; I guess I just solved for the normal force 'on the side'
Technically, it is in the k direction. Not sure what I was thinking.. your way is far more elegant than mine haha!
What did you get for you equation for the normal force?
I have:
N=(mg)cos(30). Then I am projecting this value for onto my e_r vector, which points to the left.
Essentially, my N comes out to be 8.496*mass (of course, the mass ends up being negligible). After that, my equation looks identical to yours.
I hope I haven't just embarrassed myself!
You can't assume that the normal force is just the component of the weight in the direction you need.
If you sum the forces in the k direction you get:
fsin(theta)+Ncos(theta)-mg=0
Using that equation you can solve for N, which I got to be around 7.748*mass
Absolutely right, that's brilliant. As obvious as that is, I never would have caught my error. Thanks a lot!
It makes sense, too, why I was able to get away with not summing forces in the k direction on the amusement ride problem in the last homework; the only force on the gondola (aside from gravity) was that of the supporting arm. Thanks again.
For the r direction you should have:
N*sin(theta)- f*cos(theta) = -m(r''-r*theta'^2) = -m*|r|*w^2
and y/k:
-mg + N*cos(theta) + f*sin(theta) = 0
move mg over and then divide the equations and you'll get the right answer. (f = uN)
you should end up with:
w = sqrt(x/y) where:
x = g(sin(theta)-u*cos(theta))
y = r(cos(theta)+u*sin(theta))
with how I set up my e_r, both x and y were negative numbers (e_r pointing to left).
Wow! The participation on this post has been great.
Congratulations to all who participated. You were able to get a good resolution to all the issues discussed here.
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