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Level 3 Forces Problem - Coefficient of Static Friction

  1. Feb 11, 2012 #1
    1. The problem statement, all variables and given/known data

    A coffee cup on the dashboard of a car slides forward on the dash when the driver decelerates from 48 km/hr to rest in 3.7 s or less, but not if he decelerates in a longer time.

    What is the coefficient of static friction between the cup and the dash?

    2. Relevant equations


    Final Velocity - Initial Velocity / Time
    Coefficient of Static Friction = Maximum Force of Static Friction / Normal Force
    F = ma?


    3. The attempt at a solution

    I found a. Final Velocity - Initial Velocity / Time

    a = -3.59 m/s^2

    I was going to attempt to use F = ma but I have two unknowns - mass and net force. If the coffee cup is decelerating, the direction of the net force is pointing downward. In a free body diagram, we know mg always points straight down. I also think that force is larger than the normal force because the acceleration is negative which means the direction of net force is down. Could someone give me a hint as to how I can figure out the normal force? Or if I'm doing this right at all?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 11, 2012 #2

    wukunlin

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    hint: force on the cup during deceleration equals static friction force :wink:

    if you still don't get it, write down the statement above mathematically
     
  4. Feb 11, 2012 #3

    PhanthomJay

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    The car is decelerating forward, not down. There is no acceleration in the up-down vertical direction.
     
  5. Feb 12, 2012 #4
    I still don't think I understand. I'll say left is the negative x direction and right is the positive x direction. In my free body diagram I left out vertical forces because the acceleration is occurring in the x axis. I have a force vector pointing to the left that says F = m (-3.59 m/s^2) and then one going right that says F sub k for kinetic friction. I have attached a diagram for clarification. I also noticed on my left side I'm missing a mass. Is that even relevant to this problem?
     

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  6. Feb 13, 2012 #5

    wukunlin

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    if you equate the force during decelerating to the static friction force, you will see the mass of the cup (and the normal/weight force) is irrelevant to finding the answer of this question
     
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