Will a Box Slide on a Truck During a Sharp Turn?

[alotaattitude32]

Here is the questions:
A box of mass m= 10 kg is sitting on the floor of a truck as the truck rounds a curve to the left of radius 15 m at 12 m/s. There is friction between the box and the floor of the truck with mus= .45 and muk = .20.

1. Does the box slide?
2. If the box slides, in what direction and with what acceleration?
3. If the box doesn't slide, what would the coefficient of static friction be in order for it to slide?

 

[Andrew Mason]

Here is the questions:
A box of mass m= 10 kg is sitting on the floor of a truck as the truck rounds a curve to the left of radius 15 m at 12 m/s. There is friction between the box and the floor of the truck with mus= .45 and muk = .20.

1. Does the box slide?
2. If the box slides, in what direction and with what acceleration?
3. If the box doesn't slide, what would the coefficient of static friction be in order for it to slide?

You will have to show us what you have done first. What are the forces on the box?

AM

 

[alotaattitude32]

So far i have drawn a free-body diagram with the normal force upward, and the centripetal, static friction, and kinetic friction forces drawn to the right. The force of gravity is of course pointing downward. I have calculated the Static force as being 44.1 N, the kinetic force as being 19.6 N, and the centripetal force as 96 N. I concluded that the box does slide because the centripetal force is greater than the frictional force. For centripetal acceleration i got 9.6 m/s^2. However, i was just confused as to how to calculate the acceleration when the box slides. Please help.