Energy conservation of a sliding block

[simmonj7]

Homework Statement

An 8.77-kg block slides with an initial speed of 1.58 m/s down a ramp inclined at an angle of 28.5° with the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.69. Use energy conservation to find the distance the block slides before coming to rest.

Homework Equations

E = U + K
Non conservative force = E final - E intial

The Attempt at a Solution

So I first calculated the normal force by doing N = mg cos 28.5 and found that the normal was 75.6079 N.
Then, I knew the frictional force was equal to $$\mu$$ times the normal vector so I computed that and found that this force was equal to 52.169 N.

Now I calculated E final and E initial. I figured E initial would be (1/2)mv$$^{2}$$ (U would equal 0 because d=0 initially) where v is in initial velocity stated in the problem and got that this equaled 10.9467. I figured E final would be mgd where d is the final distance we are solving for (K equals 0 because the final velocity is zero since it comes to rest) so I got this equaled 86.0337d.

Then I figured since the frictional force is the non conservative force, I would set that equal to the final energy minus the initial energy so I would get 52.169 = 86.0337d - 10.9467 so I get d = .734.

However, this apparently isn't even close to the right answer. Where am I going wrong? Any help please?

 

[panchoman]

Wnc is (mu)(normal)(d)

Why is your d in the Efinal term? It should be in your first term.

D=(86.03-10.95)/52.169

 

[ehild]

2. Homework Equations

Non conservative force = E final - E intial

This equation is wrong. The difference of energy is work or energy, not force.

 

[simmonj7]

I now see that I copied that equation wrong. I did compute the work of the frictional force not just the force and I still have the wrong answer.

But no d should not be in my E initial because at the initial point the object has not moved. Hence the distance is zero.

 

[simmonj7]

And the equation you provided for d is also no where near the correct answer, panchoman.

 

[simmonj7]

Ok so I think I get it...
Is it that the d I just solved for is the vertical distance so I need to use my angle to solve for the distance it moved down the incline?

 

[ehild]

The initial energy is 1/2 mv₀² if you count the potential energy from the top of the slope. What is the final potential energy then?

ehild