Calculating the displacement using the work-energy principle

[brycenrg]

Homework Statement

An object is traveling at 10m/s. along an inclined surface of an angle 10°. How far does it go up the bank?
How fast will it be going when it travels back down?
Coefficient of friction is .15

Homework Equations

Ei = Ef
Ef - Ei = Eloss
[/B]
W = Fd

The Attempt at a Solution

I don't really know where to start. I made a FBD.
∑Fx = gsinθ+ukgcosθ = ma
There are two unknowns. I don't know the distance. and I don't know how much energy is lost in the displacement.

If there was no friction I could solve it using Ei = Ef but with friction I don't know where tostart. Can anyone tell me the first step?[/B]

 

[brycenrg]

I tried again. 1/2mv^2 = ukmg cos∅d+mgh
h = d sin∅
(v^2)/(2g(cos∅+sin∅)) = d =32.6 m
That is the displacement. I think.
use h = dsin∅ to find initial H
use mgh = ukmgcos∅d+1/2mv^2 to find v
Is that correct?

 

[SammyS]

(Use X² icon for superscript, X₂ for subscript.)

I tried again. 1/2mv^2 = ukmg cos∅d+mgh
h = d sin∅

That's a good start.

It looks like you left μ_k out of the following equation.

(v^2)/(2g(cos∅+sin∅)) = d =32.6 m
That is the displacement. I think.
use h = dsin∅ to find initial H
]use mgh = ukmgcos∅d+1/2mv^2 to find v
Is that correct?