(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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/s^{2}. The

coefficient of friction is μ=0.75. Determine the time the first

package slips.

Answer: t_{s}=11.32s

2. Relevant 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]

3. 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 = -F_{s}+F_{pulley}=ma

Sum of forces y-dir = N-mg=0 -----> N=mg

The maximum static friction would be F_{s}=μ_{s}mg.

For polar or path coordinates, I wouldn't know where to start.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Conveyor belt and friction- Determine slip time

**Physics Forums | Science Articles, Homework Help, Discussion**