Mechanics - find the coefficient of friction

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  • #1
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Homework Statement


A horizontal force of 2 N is just sufficient to prevent a block of mass 1 kg from sliding down a rough plane inclined at arcsin [tex]\frac{7}{25}[/tex] to the horizontal. Find the coefficient of friction between the block and the plane and the acceleration with which the block will move when the force is removed.

g = 9.8


Homework Equations


F = [tex]\mu[/tex]R


The Attempt at a Solution


I didn't try the second part, but this is the first part.
Ncos[tex]\theta[/tex]+[tex]\mu[/tex]R=mgsin[tex]\theta[/tex]
I replace N and [tex]\theta[/tex] with the values given and R with mgcos[tex]\theta[/tex] and solve for [tex]\mu[/tex].

I get [tex]\mu=0.0876[/tex]

The answer at the back of the book is 0.0827 for coefficient.
1.97 ms^-2 for acceleration
 

Answers and Replies

  • #2
PhanthomJay
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Homework Statement


A horizontal force of 2 N is just sufficient to prevent a block of mass 1 kg from sliding down a rough plane inclined at arcsin [tex]\frac{7}{25}[/tex] to the horizontal. Find the coefficient of friction between the block and the plane and the acceleration with which the block will move when the force is removed.

g = 9.8


Homework Equations


F = [tex]\mu[/tex]R


The Attempt at a Solution


I didn't try the second part, but this is the first part.
Ncos[tex]\theta[/tex]+[tex]\mu[/tex]R=mgsin[tex]\theta[/tex]
I replace N and [tex]\theta[/tex] with the values given and R with mgcos[tex]\theta[/tex] and solve for [tex]\mu[/tex].

I get [tex]\mu=0.0876[/tex]

The answer at the back of the book is 0.0827 for coefficient.
1.97 ms^-2 for acceleration
You don't have all the forces listed, and your geometry/trig and sum of force component equations are off. When you do inclined plane problems, first identify all forces acting, both the gravity force and all the contact forces. Then, before applying Newton's laws, let the x axis be parallel to the incline , and let the y axis be perpendicular to the incline. Now tilt your head, break forces into their x and y components, and solve using Newton's laws in both the x direction and y direction.
And welcome to PF!
 
  • #3
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Thank you PhantomJay for the help. I forgot to include the vertical component of the horizontal force when calculating R, which affected my final answer.
 

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