Measuring the coefficient of friction

[Lobber]

What is the coefficient of friction for a metal mass sliding down a wooden slope?
Mass=0.50kg
Slope distance=1.83m
Angle=54 Degrees
Time=1.06 s
Vi=0m/s
g=9.81m/s/s
For this question we had to write out a formula and find mu.

I first found acceleration to be 3.257m/s/s, Friction force to be 4.9255N, Natural force to be 4.201N, and mu to be 1.1725.

My formula was:
D-Vi*T/0.5T^2=A
Fnetx=Fnetx
Fx=Max
Ax=(cos theta)A
Fg=mg
Fgx=mg(sin theta)
Fx=Ff-Fgx
Fx+Fgx=Ffx
Fnety=Fnety
Fy=MAy
Ay=(Sin theta)A
Fg=Mg
Fgy=Mg(cos theta)
Fy=Fny-Fgy
Fy+Fgy=Fn
Ff=mu Fn
Ff/Fn=mu

I know it have a lot of unnecessary steps in there but it is to show where my forces are coming from and what they are (my teacher is a step Nazi and everything must be written down no matter how useless and repetitive...) Now my question is whether or not that formula is correct, if my answers are correct, and if/how the formula can be shortened.

 

[sArGe99]

What is the coefficient of friction for a metal mass sliding down a wooden slope?
Mass=0.50kg
Slope distance=1.83m
Angle=54 Degrees
Time=1.06 s
Vi=0m/s
g=9.81m/s/s
For this question we had to write out a formula and find mu.

I first found acceleration to be 3.257m/s/s,

That is correct. I get the same as well.

Friction force to be 4.9255N, Natural force to be 4.201N, and mu to be 1.1725.

Friction force is 4.925 N? I think you should recheck that.

 

[sArGe99]

You needn't work out this many steps
$$mg sin\theta - \mu mg cos\theta = ma$$
After calculating acceleration, substitute the value in the above equation to get
$$\mu = \frac{mg sin\theta - ma}{mg cos\theta}$$
You can cancel out $$m$$ from the above and calculate.

 

[sArGe99]

I did and got the same answer which means I have a formula problem...

You needn't calculate frictional force at all if you're looking only for coefficient.

 

[Lobber]

Well the main purpose of the assignment to to get the coefficient but we also need the Ff and Fn and how we got to all 3 in the most basic of steps... Sign and I thought I finally had my formula...

 

[sArGe99]

Is your answer correct now? You can find out frictional force after calculating $$\mu$$

 

[Lobber]

I don't know don't have the answers for it... the answer I did get for your formula was mu=.811

 

[Lobber]

What I need it a formula that relates Fnety=MAy and Fnetx=MAx to related normal force and friction force and how the formula is derived.