# Say we have a conveyor belt with a pile of sand on top of it. What will be the maximum acceleration the belt can have before the sand start sliding? [closed]

I encountered this problem while studying for an exam later this month.

I've drawn the force diagram:

The coefficient of the rolling resistance is given as 0.50.

I know the forces acting upon the sand can be described as:

$$F_g=m\cdot g$$

$$F_1=F_g\cdot \sin (20)$$

$$F_2=F_g\cdot \cos(20)$$

$$F_n=F_2$$

$$F_{\mu}=F_n \cdot 0.50$$

How do I how do I move on from here?

Any suggestions as to what methods could be used would be very much appreciated.

• The sand slides when the force the conveyor belt applies to it exceeds the static friction which stops it from sliding. No different than a "how hard do you push a block before it slides?" Don't be fooled. – DKNguyen May 14 at 2:02
• Thanks for the answer. So if I understand correctly, the maximum acceleration would be the acceleration for which the force is equal to the friction? – BatS00p May 14 at 15:24