Kinetic Friction & Accelerating Crate: Unraveling the Mystery

[healthfreak]

1. Why does a crate on an accelerating truck accelerate backwards proportional to the amount of kinetic friction? I don't understand why the crate accelerates backwards as if kinetic friction was the only force acting on it.



2. Homework Equations :
F=ma

 

[tiny-tim]

Welcome to PF!

Hi healthfreak! Welcome to PF!

1. Why does a crate on an accelerating truck accelerate backwards proportional to the amount of kinetic friction? I don't understand why the crate accelerates backwards as if kinetic friction was the only force acting on it.
…
Relevant equations:
F=ma

Yup … good ol' Newton's second law … F = ma.

But that's a vector equation …

so it's valid in each direction individually

(in other words, you can take components in any fixed direction, and F = ma still works).

Now on a flatbed truck (I assume the floor of your truck is flat ), the only movement possible is horizontal, so the acceleration must be purely horizontal, so if you take horizontal components, then the kinetic friction is the only force acting on it!

 

[nasu]

1. Why does a crate on an accelerating truck accelerate backwards proportional to the amount of kinetic friction? I don't understand why the crate accelerates backwards as if kinetic friction was the only force acting on it.

The friction it is the only force acting on it (along the horizontal direction).
What other force do you see here?
If there is no friction, when the truck accelerates the crate will simply keep moving with constant speed (the speed of the truck right before accelerating). Relative to the ground the crate will move forward. Relative to the truck it will move backwards (and eventually fall off).
Now if you have some friction, when the crate moves backwards (relative to the truck) the friction (acting forward, right?) will slow down the motion. The acceleration is negative and is a=Ffriction/m). It will still fall off but later.