Friction Formulas: Fn, Ff & Mu w/ D, T, A, Vi & Ramp Angle

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SUMMARY

The discussion focuses on deriving the formulas for the normal force (Fn), friction force (Ff), and the coefficient of friction (μ) for an object sliding down an inclined plane. Key variables include distance (D), time (T), acceleration (A), initial velocity (Vi), and the ramp angle (θ). The user attempts to apply trigonometric functions and Newton's laws to derive the equations but struggles with the calculations. The correct approach involves understanding the components of gravitational force acting parallel and perpendicular to the ramp surface.

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Homework Statement


What is the formula for: Fn, Ff, and mu when you have a object sliding down a ramp.
Variable know are D, T, A, Vi, and the angle of the ramp above the horrizon.


The Attempt at a Solution


I've tried a few that ended up being quite long and all wrong...
 
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Lobber said:

Homework Statement


What is the formula for: Fn, Ff, and mu when you have a object sliding down a ramp.
Variable know are D, T, A, Vi, and the angle of the ramp above the horrizon.

What are D, T, A? I take it Fn is the normal force, Ff is the friction force and Vi is the initial velocity?

Lobber said:

The Attempt at a Solution


I've tried a few that ended up being quite long and all wrong...

Please could you show some of your working?

You should obtain expressions involving trig. functions and the properties of your mass.
 
D=1.83M
T=1.06S
A=3.257m/s/s
angle/theta is 54 degrees
Vi=0
M=0.5kg
Friction force?
Normal force?
Mu?

Formula#1 (didn't work...)
Ff:
(cos theta A)*M=Max=Fx
Fx=Ffx-Fgx
Fgx=(sin theta)Mg.
Fn:
Ma(sin theta) = May
May=Fy=Fny-Fgy
Fgy=M*(cos theta)g

Ff/Fn=mu

Formula2

Fx=Max
ax=a(cos theta)
Fy=May
ay=a(sin theta)
Fg=Mg
Fx=Max=Fgx-Ffx
Fgx=Mg(sin theta)
Fy=May=Fgy-Fny
Fgy=Mg(cos theta)
Ff/Fn=mu.

My answers with these two formulas were ff=4.93 Fn=4.20 mu=1.20

for formula 2 they were Ff=3 Fn=1.56 mu=1.92
 
I think I might have fixed my problem as ay=Fgy=0 so that changes things. Also it's an inclined plane question.
 
Last edited:
Your value of mu should always be less than one.

I think you need to find the difference between the actual force at the bottom and the theoretical force at the bottom.

Please could you post equations that would give the component of weight normal to the surface and the component of wieght parallel to the surface and we will go from there.

Edit: don't split it up into x and y parts, it makes things more messy.
 
Last edited:

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