Calculating Distance Traveled on an Incline with Friction

[ViewtifulBeau]

A 0.64 kg bundle starts up a 10.08° incline with 61.7 J of kinetic energy. How far will it slide up the plane if the coefficient of friction is 0.373?

I found the frictional force and the force of gravity working against the bundle by f = N*u and F = ma to be 3.6026 and 1.09886. I added those two together and divided the Work (61.7 J) by the sum to get 13.12 by W=F*D. but 13.12 m is not right. thanks

 

[hotvette]

The key to this one is that the 61.7 J of kinetic energy is just another way of stating what the initial velocity is. What's the relationship between velocity and kinetic energy?
Suggest you look at the 3rd item in the following link. It contains a sample incline plane problem (file Motion3b.pdf) using a simple methodology for solving it.
https://www.physicsforums.com/showthread.php?p=780118#post780118

EDIT: Since this is now an archive, can't post. I got the same answer as you for the initial velocity and between 18.0and 18.5m for the distance traveled. Here was the methodology I used (as described in the link):
- draw FBD and label the forces (component of mg in -x, friction force in -x)
- choose coordinate system with +x up the incline
- write F=ma in the x direction
- integrate once to get v(t) noting that v0 = velocity calculated from kinetic energy
- integrate agian to get x(t) noting that x0 = 0
- use v(t) to find t when the block stops (hint v = 0)
- use the t just calculated in the equation for x to find out how far it traveled

 

[ViewtifulBeau]

so i converted the KE to velocity and got 13.885 m/s then i found the acceleration by adding the f and F(gravity) then i used V^2 = 2a(change in x).
so 13.885^2/(2*7.346) and i got ...13.12 again!

 

[hotvette]

Now I see what you are using (work-energy). You need to account for the angle of the incline. Using work-energy and accounting for the incline, I was able to obtain the same answer as my previous post.

 

[Physwiz]

try resolving force into components...