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

In summary, when an object is sliding down a ramp with known variables D, T, A, Vi, and the angle of the ramp above the horizon, the formulas for Fn, Ff, and mu are:- Fn = Ma(cosθ)- Ff = Ma(sinθ)- Mu = Ff/FnAlternatively, the formulas can also be written as:- Fn = Mg(cosθ)- Ff = Mg(sinθ)- Mu = Ff/FnWhere M is the mass of the object, g is the gravitational acceleration, θ is the angle of the ramp, and a is the acceleration of the object. It is important to note that the value of mu should always be less than one
  • #1
Lobber
7
0

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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  • #2
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.
 
  • #3
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
 
  • #4
I think I might have fixed my problem as ay=Fgy=0 so that changes things. Also it's an inclined plane question.
 
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  • #5
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:

1. What is friction and why is it important?

Friction is the resistance force that occurs when two surfaces come into contact and move against each other. It is important because it helps us to walk, drive, and perform many other daily activities. Without friction, objects would not be able to stay in place or move smoothly.

2. What are the three types of friction?

The three types of friction are static friction, kinetic friction, and rolling friction. Static friction occurs when two surfaces are not moving relative to each other, kinetic friction occurs when two surfaces are sliding against each other, and rolling friction occurs when an object rolls over a surface.

3. What is the formula for calculating friction force (Ff)?

Ff = μ * Fn, where μ is the coefficient of friction and Fn is the normal force. The coefficient of friction is a constant that depends on the materials and surfaces in contact, while the normal force is the perpendicular force exerted by the surface on the object.

4. How does ramp angle affect friction?

Ramp angle affects friction by changing the normal force and therefore the coefficient of friction. As the ramp angle increases, the normal force decreases, resulting in a lower coefficient of friction. This means that it will be easier for objects to slide down a steeper ramp compared to a shallower one.

5. How do you calculate the coefficient of friction (μ)?

The coefficient of friction can be calculated by dividing the friction force (Ff) by the normal force (Fn). μ = Ff / Fn. This value can also be determined experimentally by measuring the force required to move an object across a surface at a constant velocity.

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