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Asinment 3

  1. Oct 9, 2005 #1
    here was the original question. in the design of a super market, there are to be several ramps connecting different parts of the store. cusomers will have to push grocery carts up the ramps. An engineer has done a survey and found that almost no one complains if the force require is no more that 50 N. Will a slope of 5 degrees be too steep, assuming a 30-kg grocery cart (full of groceries)? Assume friction can be accounted for by a coeffecient of 0.10.

    we found that 5 degrees is too high. the new question requires us to find out the actual degree. How would i find it help!!!!!!!!!!!!

    i forgot to add the the formula that should be used is as follows
    Fapp= (coefficient of friction x mass x gravity x cos thada) + (mass x gravity x sin thada)
    i need help with the trig identities part more

    PLZ solve full answer plz
     
  2. jcsd
  3. Oct 10, 2005 #2

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    Your formula is,

    Fapp = mg(sinø + μcosø)

    There are two ways of solving this - analytically or using an approximate method, e.g. Newton's method.

    Analytically
    =========
    Use the substitutions,

    sinø = 2t/(1+t²)
    cosø = (1-t²)/(1+t²)

    where

    t = tan(ø/2)

    You will end up with a quadratic in t. Solve for t, then find ø = 2*arctan(t).

    Or, if you have done Newton's method, you could do it that way.
     
  4. Oct 10, 2005 #3
    ty

    thatnks for ur help but i still dont understand what to do so i was wondering if u could coach me through it
     
  5. Oct 10, 2005 #4

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    Have you made the substitutions for sinø and cosø in the formula Fapp = mg(sinø + μcosø) ?
     
  6. Oct 10, 2005 #5
    yes

    yes i did but i cant solve for either cos thada or sin thada
     
  7. Oct 10, 2005 #6

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    You have to substitute for
    sinø = 2t/(1+t²)
    and
    cosø = (1-t²)/(1+t²)

    In Fapp = mg(sinø + μcosø), replace sinø by 2t/(1+t²) and replace cosø by (1-t²)/(1+t²).
    This will give you a quadratic int t, which you then solve for, not for ø.
    See my earlier post, #2.
     
  8. Oct 10, 2005 #7
    im really slow

    can u plz write out step by step waht to do. im really slow sir plz
     
  9. Oct 10, 2005 #8

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    tman, this is a help forum and I have given you a lot of help and advice, but you have to something yourself.

    Have you read the sticky at the top of this forum ? If not, will you please do so.

    I have given you adivice and help, now it is up to you to do some work and show me what you have done.

    All you have to do is make a substitution; show me your work and I will comment upon it.
     
  10. Oct 11, 2005 #9
    thx

    thanks for ur hellp and all and im sorry i was a pest
    i solved it differently from how u showed me tho
     
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