How Far Will Jenny Slide on Flat Ground After Sledding Downhill?

[PvtDonutDJ88]

Homework Statement

While sledding down a hill Jenny(40kg with the sled) reaches a top speed of 6m/s at the bottom. She then slides on flat ground to a stop. If the coefficient of friction between the sled and the ground is 0.04 how far will Jenny slide?

Homework Equations

V_F²=V_I²+2a\DeltaX
(\DeltaX=total distance)
V_F=V_I+at
F_N=mg
F_F=F_NU

The Attempt at a Solution

I have found F_N and got 392(F_N=mg, or F_N=(-40kg)(-9.8)=392) then found the total frictional force that was 15.68(F_F=F_NU, or F_F=(392)(.04)=15.68) I'm having problems finding the acceleration, so i can actually find the distance, how can i take the info i have now and plug it into an equation to find acceleration? If i need a different equation than i have there, please show me, I'm confused on what to do next

 

[LowlyPion]

This is a Kinetic Energy to work problem.

The KE of Jenny will be equal to the Force of friction * the distance to stop - i.e the work that friction will do to gobble up her kinetic energy and stop her.

 

[PvtDonutDJ88]

So KE=(F_F)(\DeltaX) am i looking for kinetic energy? to get my distance? or what? I'm still a little confused because i only have F_F=15.68 i still have two variables? or does KE equal something?

 

[HallsofIvy]

You know the initial speed and mass so you can calculate the initial kinetic energy.

The friction force is her weight (NOT mass) times the coefficient of friction. The work done by friction is the product of that force and the unknown distance. Set equal to the initial kinetic energy and solve for the distance.

 

[PvtDonutDJ88]

oh ok i get it thank you!