Static Friction of a Braking Truck

[Calam1tous]

Homework Statement

A crate sits unrestrained on the back of a flatbed truck traveling along a straight road at a speed of 80km/hr. The driver applies a constant braking force and comes to a stop in a distance of 22m. What is the minimum coefficient of static friction between the crate and the truck bed if the crate is not to slide forward?

I took all the given variables which are:

V_i = 80km/hr
V_f = 0km/hr
(delta)X = -22m

Homework Equations

F = ma
F_s = u_s * N
V² = V₀² + 2AX

The Attempt at a Solution

I figured that in order to get the coefficient of static friction (u_s), I would need the normal force of the crate (N) and the force of the static friction itself (F_s).

If I am correct that equation should be: F_s = u_s * N

However, I am puzzled because there's no vertical forces, so (N) should equal (mg). Yet, no mass or weight of the truck is given and I can't figure out how I would proceed with this problem using any other method.

I can also calculate acceleration using V² = V₀² + 2AX,
but I don't know what I would do with this value in relation to friction.

Am I doing it the completely wrong way or is there just something I'm not seeing? Just a simple pointer would help me greatly.

 

[collinsmark]

Hello Calam1tous,

Welcome to Physics Forums!

However, I am puzzled because there's no vertical forces, so (N) should equal (mg). Yet, no mass or weight of the truck is given and I can't figure out how I would proceed with this problem using any other method.

Just keep the mass in terms of the variable m. Trust me, you'll see what I mean later as you continue.

[Edit: added above welcome statement.]