- #1
silentwf
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Homework Statement
http://img692.imageshack.us/img692/91/1391.gif
Homework Equations
[tex] \Sigma F_{r} = ma_{r} = m(\ddot{r}-r\dot{\theta}^2) [/tex]
[tex] \Sigma F_{\theta} = ma_{\theta} = m(r\ddot{\theta} + 2\dot{r}\dot{\theta})[/tex]
The Attempt at a Solution
http://img21.imageshack.us/img21/6157/freebody.png
(The green angle is theta...couldn't write that on Paint)
I used the picture above as my free body diagram instead of the one provided by the solution (in picture in problem). I did this:
For [tex]\theta[/tex] direction:
[tex]F_{\theta} + mg\sin{\phi} - N\sin{\phi} = m(r\ddot{\theta} + 2\dot{r}\dot{\theta})[/tex]
And for r direction:
[tex] mg\cos{\phi} - N\cos{\phi} = m(\ddot{r}-r\dot{\theta}^2)[/tex]
Where [tex]\phi = \frac {\pi}{2} - \theta [/tex] and [tex] r = \frac{0.5}{\cos{\theta}}[/tex]
Plugging the numbers in, I solve that F = 1.833N and N = 6.248N
The solution book gives it as F = 1.78N and N = 5.79N
Where I'm confused
One thing I'm confused is that in the diagram the solution manual gives, they didnt draw the normal force perpendicular to the surface. I thought the basic definition of a normal force was it's supposed to be perpendicular to the surface of the object?
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