How to find coefficient of Friction? - Please help, due tomorrow.

In summary, a portable road friction testing machine is needed to assess the coefficient of friction on major roads. The design should include features such as easy change of test tire, controlled wetting of the surface, and flexible measuring capabilities. Undulations and bumpiness of the road surface must be taken into consideration to avoid inaccurate results. The machine should also specify the electronics of the measurement system and how the coefficient of friction will be calculated and reported. Various designs and examples can be found through online research.
  • #1
rum2563
89
1
The question:

The driver of a 1.2X10^3 kg car traveling 45 km/h [W] on a slippery road applies the brakes, skidding to a stop in 35 m. Determine the coefficient of friction between the road and the car tires.

Equations:

- Ff = uFn
- d = 0.5 (Vi + Vf) * time
- Fn = mg
- F = ma


My attempt:

To find normal force:
Fn = (1.2 * 10^3) (9.81)
= 11772 N


To find acceleration:
d = 0.5 (Vi + Vf) * time
35 = 0.5 (45 + 0) * time
35 = 0.5 (45) * time
35 = 22.5 * time
35/22.5 = time
time = 1.6 seconds

acceleration = (Vf - Vi) / time
= (0 - 45) / 1.6
= -28.12 m/s^2


To find force using Newtons' law:

F= (1.2*10^3)(.28.12)
= -33744 N

u (coefficient of friction) = -33744 / 11772
= -2.87

Is the answer correct?
Basically we have to find the coefficient of friction, but I am confused as to how to find it out. The main problem is that acceleration is negative, can anyone please help.
This is due tomorrow for me.

Thanks.
 
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  • #2
watch out for 45km/h...
 
  • #3
21385 said:
watch out for 45km/h...

Could you please elaborate a bit more? Thanks.
 
  • #4
divide by 3.6 to get meters per second
 
  • #5
21385 said:
divide by 3.6 to get meters per second

But I am confused. Shouldn't I divide by 1.6 because that is the time? Or is 3.6 another number? Thanks for your help, please explain.
 
  • #6
rum2563 said:
To find acceleration:
d = 0.5 (Vi + Vf) * time
35 = 0.5 (45 + 0) * time
35 = 0.5 (45) * time
35 = 22.5 * time
35/22.5 = time
time = 1.6 seconds

acceleration = (Vf - Vi) / time
= (0 - 45) / 1.6
= -28.12 m/s^2
Careful with units! Convert the car speed to m/s.
The main problem is that acceleration is negative, can anyone please help.
Nothing wrong with a negative acceleration--the car is slowing down. The sign merely specifies direction--when computing the coefficient, consider magnitudes.
 
  • #7
The standard units for velocity is m/s. The velocity used in the question is in km/h. The other units used in the question is in meters and naturally, you would want meters per second. You have to convert the velocity to get a correct answer. To convert 45 km/h (1000m/1km)(1 h/3600 seconds) ===> 45 km/h divided by 3.6 would get you 12.5 m/s, which is what you want.
 
  • #8
So when I convert 45 km/h to m/s, I get 12.5 m/s

So do I use 12.5m/s to get the acceleration just like I did in my question?
 
  • #9
yep, that should give you the correct answer
 
  • #10
One more question, when I do all the calculations, I get a negative acceleration. So therefore, I would get a negative value for coefficient of friction. Is that OK, or would it not make sense because friction cannot be negative.

This is what I am doing:

u = -9378 / 11772
= -0.8

Please help, thanks.
 
  • #11
Friction, a force, can certainly be "negative". Remember: sign just refers to direction.

But the coefficient of friction cannot be negative: Ff = uFn describes the magnitude of the friction force, not the direction or sign.
 
  • #12
rum2563 said:
The main problem is that acceleration is negative, can anyone please help.
Thanks.

I believe that a negative acceleration just means you are slowing down in whatever direction you called positive or, you are speeding up in the direction you called negative
 
Last edited:
  • #13
Arite, thank you very much. But can you tell me that do I have to plug in 12.5m/s OR 45km/h in the formula which I am using to find time? Because I use 12.5m/s I get a lower value for u, and if I use 45km/h I get a higher value for u.

Thanks.
 
  • #14
plug in 12.5 m/s, and that will get you the correct answer
 
  • #15
Yep, I got it.

Thank you very much for all the people who have helped me in this topic. I cannot believe how quick the responses and the help was. I think PhysicsForums are a great resource and I hope I can contribute more to it. Thanks to all the people. :rolleyes:
 
  • #16
And what was your answer?
I got an answer and I need to make sure about it.. Can u please help me??
 
  • #17
Road Friction Testing Machine
Test are carried out periodically on major roads to assess their friction (accumulations if oil and rubber can seriously reduce the coefficient of friction).
You are required to design a suitable portable rig to carry out such tests that can be deployed from the back of a van or a estate car.
Your design should include a range of capabilities, i.e. easy change of test tyre – assuming you are using a test tyre; the ability to artificially wet the surface in a controlled manner and flexible measuring capabilities.
As well as the basic mechanical design of the system, you will need to consider how undulations and bumpiness in the road surface can be treated to avoid inappropriate results.
You will need to specify the electronics of the measurement system and how the coefficient of friction will be calculated and reported.

Anyone can help me?
 

1. What is the coefficient of friction?

The coefficient of friction is a measure of the amount of resistance between two surfaces in contact with each other. It is a dimensionless number that ranges from 0 to 1, with higher values indicating a greater amount of friction between the two surfaces.

2. How do I calculate the coefficient of friction?

The coefficient of friction can be calculated by dividing the force required to move an object over a surface by the weight of the object. This can be expressed as μ = F/W, where μ is the coefficient of friction, F is the force required, and W is the weight of the object.

3. What are the factors that affect the coefficient of friction?

The coefficient of friction can be affected by several factors, including surface roughness, temperature, and the type of materials in contact. Additionally, the coefficient of friction can vary depending on the force being applied and the speed of movement between the two surfaces.

4. How can I measure the coefficient of friction?

The coefficient of friction can be measured using a variety of methods, including using a force sensor to measure the force required to move an object over a surface, or using an inclined plane to measure the angle at which an object begins to slide. There are also specialized instruments, such as tribometers, that are specifically designed to measure the coefficient of friction.

5. Why is the coefficient of friction important in science and engineering?

The coefficient of friction is an important concept in science and engineering as it helps us understand and predict the behavior of objects in motion. It is particularly relevant in fields such as material science, mechanical engineering, and physics, where understanding the forces between two surfaces is crucial in designing and creating efficient and effective systems and structures.

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