What is the acceleration of a sliding box in a decelerating truck?

[tralblaz]

First, I will state the problem -
A hauling truck is traveling on a level road. The driver suddenly applies the brakes, causing the truck to decelerate by an amount (g/2). This causes a box in the rear of the truck to slide forward. If the coefficent of sliding friction between the box and the truckbed is (1/3), find the acceleration of the box relative to (a) the truck and (b) the road.


Okay, here is what I have thus far - 1) part (a) will be a noninertial observer and part (b) will be an inertial observer. (So, I will have two equations) 2) The force(s) is in the horizontal direction and since it is DECELERATION, the horizontal force will be negative. 3) I am trying to solve this by starting with the sum of the forces, but I am not given a mass. I am only given friction and deceleration. I am assuming that g is gravitity. I also know the equation F=mA+ma'. Where a' is the acceleration of the object in the moving system.

Could anyone give me any direction on how to pursue this problem? THANKS!

 

[Fermat]

Suppose initially that there is no friction inside the truck, and both truck and box are traveling at the same speed, therefore motionless wrt each other.
Now when the truck decelerates, and there is no friction to stop the box, then it will accelerate at g/2 wrt the truck.

What is the force required to act on the box in order to give it this accln?

Now you know the accelerating force, add in friction. etc.

 

[tralblaz]

Thanks :)