- #1

JJBladester

Gold Member

- 286

- 2

## 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/s

^{2}. The

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

package slips.

Answer: t

_{s}=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 = -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.