Conservation of energy of a toboggan problem

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

-.12m/s

djeitnstine
Gold Member
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.

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

Ah of course. I knew that. Thanks!