How to find the maximum acceleration given coefficient of static friction and mass

  1. 1. The problem statement, all variables and given/known data
    A flatbed truck is carrying a 20.0-kg crate along a level road. The coefficient of static friction between the crate and the bed is 0.400. What is the maximum acceleration that the truck can have if the crate is to stay in place?

    2. Relevant equations
    Is the equation to solve for maximum acceleration F s,max= usN * us?


    3. The attempt at a solution
    I was not taught how to do problems like this...not 100% sure what to plug in for usN...I gave it a shot:
    The surface is flat, so I guess the normal force=20.0 kg, so I then mulitplied by .40 to get 8 m/s.........ahhhh. I don't know what I'm doing!

    Thanks in advance.
     
  2. jcsd
  3. PhanthomJay

    PhanthomJay 6,187
    Science Advisor
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    Gold Member

    Fsmax = usN. Then use Newton's 2nd law.
    20 Kg, is the mass, the normal force is its weight. Use formula that relates weight with mass.
     
  4. uh, hmm. I looked through my notes, couldn't find this kind of formula.

    What am I to do to solve this problem? I looked at the F s, max formula wrong, so it's us times N. I was initially puzzled by usN times us. Now it makes since.

    So, us= .40 right? But I don't know how to get the weight of 20kg for normal force, N.

    Thanks
     
  5. PhanthomJay

    PhanthomJay 6,187
    Science Advisor
    Homework Helper
    Gold Member

    The normal force on the crate, in this problem, is equal to the weight, since there is no acceleration vertically and only the weight and normal forces act in the vertical diretion, so they must be equal and opposite in satisfaction of newton's 1st law. Now weight is just the force caused by the acceleration of gravity, please memorize it, W=mg, where g is the acceleration of gravity where g is equal to 9.8m/s/s on the earth's surface. When the mass is in kilograms, the weight, using this formula, is in newtons. 20 Kilograms weighs 196 newtons.
     
  6. so my answer will be .40 times 196 N which is 78 m/s^2?!
     
  7. Re: How to find the maximum acceleration given coefficient of static friction and mas

    A flatbed truck is carrying a 20.0-kg crate along a level road. The coefficient of static friction between the crate and the bed is 0.400. What is the maximum acceleration that the truck can have if the crate is to stay in place?

    f=ma for (m) moving direction
    R=ma
    F=mg
    coeffi.fric=F/R=mg/ma
    a=g/coeff.fri
    = 10/0.4m/s2
    =25m/s2
     
    Last edited: Jul 15, 2011
  8. Re: How to find the maximum acceleration given coefficient of static friction and mas

    I love this problem and since I am a flatbed driver I have a more interesting one:

    48 feet flatbed
    6000 pounds load 8 feet high (the load is full trailer)
    A flatbed is 8.5 feet whide
    driver will drive at 65 miles per hour (there is no wind)

    How many straps and how tiht should they be so he does not lose everything in 600 miles :D

    (I'm a geek flatbed driver... If I get an answer to this I will post more)
     
    Last edited: Dec 7, 2011
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