Static and dynamic(kinetic) coefficients of friction

In summary, the three surfaces studied had different coefficients of static friction, with wood having the highest value and metal having the lowest. To calculate the coefficient of dynamic friction, the object was nudged at a constant speed so that it would not stop or accelerate. When the angle was increased until the object did not stop or accelerate, the angle was found to be 37.3° for wood, 18.0° for glass, and 14.7° for metal.
  • #1
thestudent101
21
0
I have a Mathematics C assignment, with one question being about static and dynamic friction. But I think it fits this forum. Anyway, we need to conduct experiments to show if there is a difference between static and dynamic friction or not with three different surfaces.The weight of the object being tested is 0.0685kg and gravity has been assumed as -9.8m/s^2I have calculated the coefficient of static friction for the three surfaces. This was done so by placing an object of weight 0.0685kg on a surface and increasing the angle until the object starts to slide. For wood, the average angle was 37.3°, for glass - 18.0° and for metal - 14.7°. For calculating the static coefficient of friction the weight force has been calculated as
w=mg
w=0.0685*-9.8
w=-0.6713 Newtons

This has then been subbed into
0=wsinθ-Fr
0=-0.6713*sin(37.3)-Fr
Fr= 0.407 Newtons

0=-wcosθ+N
0=-(-0.6713*cos(37.3))+N
N=0.534 Newtons

μ=Fr/N
μ=0.407/0.534
μ=0.762 (wood)
This process has been repeated for glass (μ=0.324) and for metal (μ=0.263)

Now I am completely stuck on how to calculate the coefficient of dynamic friction. I was thinking about timing how long the object takes to slide down a certain length from a set angle? But I don't know how to calculate the coefficient from that? Any ideas and help will be appreciated thanks.
 
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  • #2
You might note from your correct calculations that the static coefficient of friction is simply u_s = tan theta, which you can deduce using letter variables instead of plugging in numeric results. Does this give you a hint as to how you might calculate the dynamic coefficient of friction without using a clock or meter stick?
 
  • #3
The friction and normal force also need to be calculated so that's why I did it that way. But no, unfortunately that didn't give me any hints.
 
  • #4
How about if the object slides down the incline at constant velocity (no acceleration)?
 
  • #5
i still don't know how to incorporate that into it.
 
  • #6
thestudent101 said:
i still don't know how to incorporate that into it.

I am not familiar with what is covered in Maths C. You could certainly do it the way you suggested, that is,
I was thinking about timing how long the object takes to slide down a certain length from a set angle?
where knowing the time, length, and angle, you can calculate the acceleration, then use Newton's second law, F_net =ma, to solve ultimately for the kinetic friction coefficient. If you are familiar with this method, this will work fine, with the usual error in the time measurement.

On the other hand, you seem to be familiar with Newton's 1st law, which says the net force is zero when an object is not moving (or just about to move). That's how you calculated the coef of static friction (u_s =tan theta). Newton's first law also says that the net force is 0 if an object is moving at constant velocity. So the same equations apply, only this time you must adjust the angle such that the object is moving at constant speed without accelerating. u_k is always equal to or less than u_s, almost always less. Can you think of a way to find this angle such that u_k = tan theta when the object is moving at constant speed ??
 
  • #7
what's u_s and u_k?
that's probably a really stupid question.
 
  • #8
u_s is coefficient of static friction, while u_k is coefficient of kinetic friction.
 
  • #9
thestudent101 said:
what's u_s and u_k?
that's probably a really stupid question.
Oh, sorry, u_s is the coefficient of static friction, and u_k is the coefficient of kinetic (dynamic) friction. I should have written it in LateX [itex]\mu_s[/itex] and [itex]\mu_k [/itex]
 
  • #10
T+Wsin(theta)-Fr+n-Wcos(theta)=ma
T+Wsin(theta)-Fr+n-Wcos(theta)=0
Therefore -Wcos(theta) and N are the same.
T+Wsin(theta)-Fr=0
I'm soooo confused now.
 
  • #11
thestudent101 said:
T+Wsin(theta)-Fr+n-Wcos(theta)=ma
T+Wsin(theta)-Fr+n-Wcos(theta)=0
Therefore -Wcos(theta) and N are the same.
T+Wsin(theta)-Fr=0
I'm soooo confused now.
You need to look along the incline direction only when the object is accelerating; it is not accelerating perpendicular to the incline, so you still have N = mgcostheta in that direction. And what is T? No such force exists. Your first equation should read Wsintheta - Fr = ma. Where Fr = u_k(N).

But why go through all the maths when you can simply start at a small angle and give the object a nudge so it starts sliding. it will quickly stop. So then increase the angle and nudge it again. See if it still stops. keep on increasing the angle until it doesn't stop. Play around with it. When it neither stops or accelerates, that's the angle you want. And you don't have to fool with Newton 2, because it's moving at constant speed, so you have, at that angle, Wsintheta -Fr = 0, as before.
 
  • #12
Ok, so I did what you suggested. I used the formula wsintheta-Fr=ma and n=wcostheta.
Here's the results.
Wood (static): 0.762
Wood (kinetic): 0.345
Glass (static): 0.324
Glass (kinetic): 0.212
Metal (static): 0.263
Metal (kinetic): 0.140

Do these values seem reasonable?
 
  • #13
The friction coefficients depend on the material of the 2 contact surfaces, the cleanliness of the surface, whether it is dry or moist, etc. . You do not indicate what material the obect on the incline is made of, so I don't know if your calculated coeffficients, both static and dynamic, are reasonable. Could be a lot of lab errors. Compare your results to published tables for these values.

Try your experiment again. And again. The tangent of the angle at which it just starts to move is the static coefficient friction. The tangent of the angle at which it slides at constant speed after being 'nudged', is the kinetic coefficient. Start with small angles and slowly increase the angle until these events occur.
 

1. What is the difference between static and dynamic coefficients of friction?

The static coefficient of friction refers to the amount of force needed to overcome the initial static friction and set an object in motion. On the other hand, the dynamic coefficient of friction refers to the amount of force needed to maintain the motion of an object.

2. How are static and dynamic coefficients of friction measured?

Static and dynamic coefficients of friction are typically measured by using a device called a tribometer, which measures the force required to move an object across a surface.

3. What factors affect the static and dynamic coefficients of friction?

The coefficients of friction are affected by the nature of the two surfaces in contact, the roughness of the surfaces, and the presence of any lubricants. The weight and shape of the object can also impact the coefficients of friction.

4. What are some real-life applications of understanding static and dynamic coefficients of friction?

Understanding the coefficients of friction is important in designing and improving machines, such as engines and brakes, as well as in developing new materials for various industries. It also plays a crucial role in preventing accidents, such as slips and falls, by identifying potential hazards.

5. Can the coefficients of friction be altered or controlled?

Yes, the coefficients of friction can be altered or controlled by changing the surface properties, such as using lubricants or changing the roughness of the surfaces. The weight and shape of the object can also be adjusted to affect the coefficients of friction.

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