Mastering Physics: Kinetic and Static Friction

In summary, the conversation discusses finding the minimum angle at which a box starts to slip on an inclined plane, given its mass, coefficients of kinetic and static friction, and the equations for the normal force and frictional force. The solution involves using the equation m*g*sinθ = μ*m*g*cosθ and taking the arctan to determine the angle.
  • #1
rwcollings
5
0

Homework Statement



A box of textbooks of mass 24.5 rests on a loading ramp that makes an angle with the horizontal. The coefficient of kinetic friction is 0.260 and the coefficient of static friction is 0.360.

As the angle is increased, find the minimum angle at which the box starts to slip.

Homework Equations



N+fs+W=0

N=mg cos[tex]\vartheta[/tex]
fs=mg sin[tex]\vartheta[/tex]

The Attempt at a Solution



In my notes, it gives an example of an object at rest on an inclined plane and sets up the two above equations with the angle and weight of the object both given. The problem is that when I add up the three forces N, fs, and W I do not get "0". This is leaving me quite confused.

I have tried substituting the equations above into the top equation equal to zero, but I cannot figure out how to solve for theta since Weight is involved.

Can anyone give me a push in the right direction. I feel like I am forgetting something.
 
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  • #2
Welcome to PF.

You must remember that the frictional force is really only a maximum number that needs to be overcome in order for there to be motion along the incline.

Hence what you need to consider is the point at which your

m*g*sinθ = μ*m*g*cosθ
 
  • #3
Thank you for the quick response (sorry for my delay). So what does the symbol "μ" represent in the equation? Will I be able to set the equation equal to zero and factor out the common angle?

Thanks,

Rob
 
  • #4
rwcollings said:
Thank you for the quick response (sorry for my delay). So what does the symbol "μ" represent in the equation? Will I be able to set the equation equal to zero and factor out the common angle?

[tex]\mu}[/tex] is the coefficient of friction. And the rest you got right.
 
  • #5
LowlyPion said:
Hence what you need to consider is the point at which your

m*g*sinθ = μ*m*g*cosθ

In this equation both mg are the same correct? So that would make μcosθ=sinθ

I realize looking at this that I can't just factor out that angle. Is there a way to determine at what angle the book is no longer stationary short of plugging in random angles?
 
  • #6
rwcollings said:
In this equation both mg are the same correct? So that would make μcosθ=sinθ

I realize looking at this that I can't just factor out that angle. Is there a way to determine at what angle the book is no longer stationary short of plugging in random angles?

Have you run across the trig identity that Tanθ = Sinθ/Cosθ before?
 
  • #7
Yes, thanks for the reminder. That's one of those things that you end up smacking yourself in the head.
 
  • #8
So ... for θ just take the arctan

Tan-1(X) = θ
 
  • #9
Yep, got the answer and it was correct.

Thank you for the help
 

Related to Mastering Physics: Kinetic and Static Friction

1. What is the difference between kinetic and static friction?

Kinetic friction refers to the force that resists the motion of an object when it is already in motion. Static friction, on the other hand, refers to the force that prevents an object from moving when a force is applied to it.

2. How do you calculate the coefficient of friction?

The coefficient of friction can be calculated by dividing the force of friction by the normal force between two surfaces. It can also be found experimentally by measuring the force required to move an object and dividing it by the weight of the object.

3. What factors affect the magnitude of friction?

The magnitude of friction is affected by the types of surfaces in contact, the force pressing the surfaces together, and any lubricants or contaminants present on the surfaces.

4. How does friction affect the motion of an object?

Friction can either slow down or prevent the motion of an object. It can also cause an object to change direction or rotate, depending on the direction of the applied force.

5. How can friction be reduced?

Friction can be reduced by using lubricants, such as oil or grease, between two surfaces. Additionally, polishing or smoothing the surfaces can also decrease friction. In some cases, adding wheels or ball bearings can also reduce friction.

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