Coefficient of friction question

In summary, the conversation discusses how a car's wheels being locked during emergency braking can cause the car to slide along the road. The record for the longest skid marks on a road was set in 1960 at 290m. Using the given values of \mu = 0.6 and g = 9.8m/s2, the formula \SigmaF = ma is used to calculate the acceleration a. Substituting a into the kinematic equation, the car's initial velocity, Vi, is calculated to be 58.3986m/s in the opposite direction of its motion. This indicates that the car was decelerating during the emergency braking.
  • #1
wtfcat
2
0

Homework Statement



If a car's wheels are locked during emergency braking, the car slides along the road. The record for the longest skid marks on a road was reportedly set in 1960. the marks were 290m long. assuming that [tex]\mu[/tex] = 0.6, how fast was the car going when the wheels became locked?

Givens:
Vf = 0m/s
Vi = ?
d = 290m
a = ?
[tex]\mu[/tex] = 0.6
g = 9.8m/s2

Formulas:
[tex]\Sigma[/tex]F = ma
[tex]\mu[/tex]k = Fk/Fn
Vf2 = Vi2 + 2ad


Homework Equations



1. Am i missing anything? Givens, formulas, etc.
2. Are my steps correct? ex. in my steps, am i missing a positive or negative sign, did i get units right, etc
3. Is my answer correct?


The Attempt at a Solution



So in this case, [tex]\Sigma[/tex]F = Fk, correct? And Fk = [tex]\mu[/tex]kmg, so ma = [tex]\mu[/tex]kmg, and cancelling out the m gives me a = [tex]\mu[/tex]kg. so a = (0.6)(9.8) = 5.88m/s2.
i sub "a" into the kinematic equation: Vf2 = Vi2 + 2ad ---> 0 = Vi2 + 2(5.88)(290) ---> -Vi2 = 3410.4 ---> -Vi = 58.3986m/s

If it's negative Vi, then does that mean that it was going backwards or something, or am i missing something here? Thanks in advance for taking the time to help me out! :biggrin:
 
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  • #2
No, you did everything right except that your car is decelerating so your a value should really be -5.88 and that would give you a positive vi value.
 
  • #3
oh, ok, got it =)
thank you!
 

1. What is the coefficient of friction?

The coefficient of friction is a value that represents the amount of resistance between two surfaces in contact with each other. It is a dimensionless number that ranges from 0 to 1, with 0 indicating no friction and 1 indicating maximum friction.

2. How is the coefficient of friction measured?

The coefficient of friction is typically measured by conducting an experiment where one surface is placed on top of the other and a force is applied to cause the surfaces to move. The force and resulting movement are then used to calculate the coefficient of friction.

3. What factors affect the coefficient of friction?

The coefficient of friction can be influenced by several factors, including the types of materials in contact, the roughness or smoothness of the surfaces, the amount of force applied, and the presence of any lubricants or contaminants.

4. Why is the coefficient of friction important?

The coefficient of friction is an important concept in many fields, including engineering, physics, and materials science. It helps us understand the behavior of objects in contact and can be used to predict how much force is needed to move one surface over another.

5. Can the coefficient of friction be changed?

Yes, the coefficient of friction can be altered by changing the factors that affect it. For example, using a lubricant can reduce friction between two surfaces, while increasing the roughness of a surface can increase the coefficient of friction.

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