How Do You Calculate the Frictional and Coupling Forces for a Skidding Truck?

[winblowzxp]

1.The 2-Mg truck is traveling at 15 m/s when the brakes
on all its wheels are applied, causing it to skid for a distance of
10 m before coming to rest. Determine the constant horizontal
force developed in the coupling C, and the frictional force
developed between the tires of the truck and the road during
this time. The total mass of the boat and trailer is 1 Mg.

v₀ = 15 m/s
s = 10 m
F_k = µ_kN

2. I'm not exactly sure how/where to start. I also have no idea how to get the frictional force.

The Attempt at a Solution

I figure that since I know v₀ and v_f as well as s₀ and s_f that I can get deceleration.

I'll use v² = v₀² + 2a(s-s₀). If I solve for a, maybe that will help get the frictional force?

 

[tiny-tim]

welcome to pf!

hi winblowzxp! welcome to pf!

I'll use v² = v₀² + 2a(s-s₀). If I solve for a, maybe that will help get the frictional force?

yes, that will give you the deceleration …

then draw two free body diagrams, one for the truck and one for the trailer, and do F = ma for each …

what do you get? ​

 

[winblowzxp]

I get:

F_B = -11.25 kN
F_T = -22.5 kN

I figure that to get the force in the coupling (C), that I need to subtract F_B from F_T which would give me F_C = -11.25 kN



I know that f_k = µN and that N in this case is -W. I'm not sure how to get the value for µ.
[PLAIN]http://www.fission-systems.com/images/physics/fma.png


Edit: I think I'll assume that it's on dry concrete and use µ_k = 0.8.

 

[tiny-tim]

i'm really not following that

µ is irrelevant, the forces can be found from the masses and the acceleration

your F = ma equations don't seem to include the force in the coupling (between the truck and the trailer)

 

[winblowzxp]

your F = ma equations don't seem to include the force in the coupling (between the truck and the trailer)

I'm not exactly sure how to do that.

 

[tiny-tim]

the trailer has only one horizontal force on it, the truck has two

(i'm assuming that the trailer wheels are not skidding, and that their moment of inertia is sufficiently small that you can ignore the friction)