File cabinet sliding in truck bed during braking

[acpyrus]

A pickup truck with a steel bed is carrying a steel file cabinet. If the truck's speed is 15 m/s, what is the shortest distance in which it can stop without the file cabinet sliding?

*---*--*-*
v(i)=15m/s
v(f)=0
Need to find x(f)

Friction: f(s) should be F(net) = 0?

Not sure where to start.

 

[dekoi]

Are you given a coefficient of friction for the cabinet?
Are you given any other information, such as masses?

I just reread the question:

I think you need to find the coefficient yourself, for steel on steel.

 

[acpyrus]

Coeffiecient of friction is not given on the problem, however I did find a steel-on-steel f(s) in a table in our text --> where f(s) = 0.80

 

[dekoi]

I am pretty sure the question should be solved as such:

The only force on the cabinet is the static friction.
Due to the cabinet's inertia (since it is already moving forward), the net force is not equal to zero. We want the friction force to move the cabinet in the opposite direction of motion so that it will not slide.

Net force on the cabinet:
Fnet = Fs

ma = μmg
a = μg

Use a kinematics equation to solve for distance, using the calculated acceleration and the known change in velocity.

 

[acpyrus]

I came up with 14.3m - which is correct. Thanks.