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Work scalar ?

  1. Sep 17, 2010 #1
    Hi, I'm a bit confused on how 'work' can be scalar. I understand that W=FSCosX where X is the angle between the point of application of force and the object. So if the Work depends upon the angle, shouldn't that mean it depends on direction of force applied making it a vector? I'm a high school student so please don't kill me because I'm honestly confused.
  2. jcsd
  3. Sep 18, 2010 #2

    Vanadium 50

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    In what direction does work point?
  4. Sep 18, 2010 #3
    You are nearly there, but look more closely at your formula.

    A vector, multiplied by a number is still a vector.

    cosX is a number so any single vector, multiplied by cosX is a vector.

    But in your formula both F and S are vectors.

    So you have two vectors multiplied together and their product multiplied by cosx.

    Whenever you have this situation the result is a scalar.
  5. Sep 18, 2010 #4
    Force is a vector (3D). The "difference" from point A to B can be called a vector (d=(x1,y1,z1)-(x2,y2,z2)). Between, there is a so called scalar product. Meaning:
    Fx * dx + Fy * dy + Fz * dz = W (Work). Do you understand that the scalar product between vectors is a number and in this case: Work is scalar?
    If not, try in mind to move a body where you live. Take the body and have a nice trip to Regensburg in Germany. Move the body there (cheaper to do it in your neighboorship but nevertheless a nice journey). The energy you will spend is the same. And the direction is not important, there is no east or west or north or south energy.

    Best regards,
  6. Sep 18, 2010 #5
    F.Scos x=W
    S is displacement i.e. a vector quantity
    Scosx is also a vector
    F is force i.e. a vector
    u must remember that the dot product of two vectors is scalar
    thus W=F.S cosx is a scalar quantity
  7. Sep 18, 2010 #6


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    if you look at the two lines above, the dot product is like asking how much the top line lays over the bottom line. As you change the angle between the two lines, you will have different lengths of overlap (the "projection" it's called, since you're essentially measuring the length of the shadow the top line casts on the bottom line). No direction required to answer that question.
  8. Sep 18, 2010 #7
    yeah absolutrly pythagorean
  9. Sep 19, 2010 #8
    Okay so the product of two vectors is scalar and thus Work is scalar. Am I right?
  10. Sep 19, 2010 #9


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    Not all products; the dot product, often called the scalar product.
  11. Sep 19, 2010 #10

    Andy Resnick

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    Can I check that the right question was (already well) answered?

    Are you asking why work (i.e. *energy*) is a scalar, or are you asking why 'FSCosX' is a scalar?
  12. Oct 16, 2010 #11
    I am asking why Work is scalar but I think I understand it now.
  13. Oct 16, 2010 #12
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