- #1
JJBladester
Gold Member
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Homework Statement
A series of small packages is moved by a conveyor belt that passes
over a 300mm radius pulley. The belt starts from rest at t=0 and its
speed increases at a constant rate of 150 mm/s2. The
coefficient of friction is μ=0.75. Determine the time the first
package slips.
Answer: ts=11.32s
Homework Equations
[tex]V_{0}=0[/tex]
[tex]r_{pulley}=300mm[/tex]
[tex]a_{pulley}=150mm/s^{2}[/tex]
[tex]\mu=0.75[/tex]
These are equations for polar coordinates, which I'm thinking I may need to use to solve the problem.
[tex]F_{r}=ma_{r}[/tex]
[tex]F_{\theta}=ma_{\theta}[/tex]
[tex]F_{net}=F_{r}{\bf e}_{r}+F_{\theta}{\bf e}_{\theta}[/tex]
[tex]m(\ddot{r}-r\dot{\theta}^{2})=F_{r}[/tex]
[tex]m(r\ddot{\theta}+2\dot{r}\dot{\theta})=F_{\theta}[/tex]
The Attempt at a Solution
First of all, I'm trying to decide if I should use cartesian, polar, or path coordinates for this problem.
If cartesian coordinates work, then I would set the problem up as below. Also, I don't think the radius of the pulley would matter...?
Sum of forces x-dir = -Fs+Fpulley=ma
Sum of forces y-dir = N-mg=0 -----> N=mg
The maximum static friction would be Fs=μsmg.
For polar or path coordinates, I wouldn't know where to start.