Calculating Wood Friction on Metal: Solving for Time

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To solve for the time it takes for a piece of wood to slide down a metal incline, the key is to calculate the forces acting on the wood, including gravitational force, normal force, and frictional force. The equations of motion, particularly ΔX = ViT + 0.5at², are essential for determining acceleration and time. The user has attempted to derive the net force but is struggling with the calculations, consistently arriving at an incorrect time of approximately 9.6 seconds. The discussion emphasizes the need to analyze the components of weight parallel and perpendicular to the incline, as well as the relationship between net force and mass. Clarifying these components and correctly applying Newton's second law will lead to the accurate solution.
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Homework Statement


You place a piece of wood onto a 227cm long piece of metal on a 25 angle. The \mu=.34 How long does it take for the piece of wood to reach the bottom of the metal?

Homework Equations


\DeltaX=227
Vi=0
a=?
t=?

\DeltaX=ViT+.5at^2
227=.5at^2

a=Fnet/m
\mu=Ff/Fn

The Attempt at a Solution


I have 2 pages of work for this problem and it's obvious to me that I'm missing something crucial. I tried this problem a few times, the first time I calculated the wrong \mu and the second time I have no idea what happened

I can't reproduce my free body diagram for you but I can tell you what I broke the components down into:
Fg=y'/sin25
Fg=x'/cos25
 
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You need to find the acceleration. To do that, you'll need the net force and Newton's 2nd law.

Try to give symbolic answers (not numbers) to these questions:

What are the components of the wood's weight parallel and perpendicular to the incline?

What's the normal force between the surfaces?

What's the friction force acting on the wood?

What's the net force acting on the wood?
 
Thats what I ended up doing but my answer came out to be 9.7 seconds, which is extremely wrong.

If I leave a as Fnet/m I end up with T=sqrt(454m/Fnet) So then I need to solve for Fnet in a way in which m cancels out (thats what my teacher said atleast). So Fnet=Fn-Ff
Fg=Ff/sin25
Fg=Fn/cos25

Fn=Fgcos25
Ff=Fgsin25

EDIT: Just worked it out that way and got the same answer 9.6 seconds... which is horribly wrong... any ideas?
 
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Why don't you try answering my questions?
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .

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