Conservation of energy of a toboggan problem

[Todd88]

Homework Statement

A loaded 305kg toboggan is traveling on smooth horizontal snow at 4.60m/s when it suddenly comes to a rough region. The region is 9.00m long and reduces the toboggan's speed by 1.10m/s.

Homework Equations

What average friction force did the rough region exert on the toboggan?

The Attempt at a Solution

I know you can find the initial conditions of the kinetic energy and then the final conditions given the final velocity. I just don't know how to get the force of the rough region. Any help is appreciated.

 

[djeitnstine]

How much average deceleration of the toboggan was there? You have the initial v, final v and the distance it decelerated by.

 

[Todd88]

-.12m/s

 

[djeitnstine]

Is that negative velocity? Check your units. Also in the case that is acceleration, then where is the problem of finding the average force of friction? $$\bar F_f=m \bar a$$ where a is the average deceleration experienced.

 

[Todd88]

It would be simple but am I correct in saying the average acceleration (deceleration in this case) is -.12m/s^2? Because when I do -.12*305 it is not correct. The friction force would be -37.3N which is incorrect.

 

[djeitnstine]

The correct formula to find acceleration with a distance, and 2 velocities is $$v^2_f=v^2_i+2ax$$ x=distance, a=acceleration

 

[Todd88]

Ah of course. I knew that. Thanks!