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Find the magnitude of a force

  1. Feb 5, 2008 #1
    [SOLVED] find the magnitude of a force

    1. The problem statement, all variables and given/known data

    A window washer pushes his scrub brush up a vertical window at constant speed by applying a force [tex]\vec{F}[/tex] as shown in the figure. The brush weighs 12.1 N and the coefficient of kinetic friction is 0.110.

    [​IMG]


    2. Relevant equations

    1. [tex]\Sigma[/tex][tex]\vec{F}[/tex] = m[tex]\vec{a}[/tex]

    2. [tex]\Sigma[/tex][tex]\vec{Fx}[/tex] = max

    3. [tex]\Sigma[/tex][tex]\vec{Fy}[/tex] = may

    4. fk = [tex]\mu[/tex]kn

    5. [tex]\vec{F}[/tex] = [tex]\sqrt{Fx^2+Fy^2}[/tex]

    3. The attempt at a solution

    [tex]\Sigma[/tex]Fx = -Fcos53.1 + fk = 0

    [tex]\Sigma[/tex]Fy = N + Fsin53.1 - w = 0

    Fcos53.1 = fk

    --> Fcos53.1 = [tex]\mu[/tex]kn

    N = w-Fsin53.1

    ---> Fcos53.1 = [tex]\mu[/tex]k(w-Fsin53.1)

    --> Fcos53.1 = [tex]\mu[/tex]kw-[tex]\mu[/tex]kFsin53.1

    --> Fcos53.1 + [tex]\mu[/tex]kFsin53.1 = [tex]\mu[/tex]kw

    --> F(cos53.1 + [tex]\mu[/tex]ksin53.1) = [tex]\mu[/tex]kw

    --> F = [tex]\mu[/tex]kw / (cos53.1 + [tex]\mu[/tex]ksin53.1)

    --> N = Fcos53.1/[tex]\mu[/tex]k

    my answer was F = 1.9N, which was wrong and I was so sure I did everything right.

    if anybody can offer any help it would be greatly appreciated.
     
  2. jcsd
  3. Feb 5, 2008 #2

    Tom Mattson

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    Staff Emeritus
    Science Advisor
    Gold Member

    The frictional force points in the y direction opposite the motion of the scrubber head, and the normal force points in the x direction, normal to the wall (that's why it's called the normal force!).

    You've got them backwards.
     
  4. Feb 5, 2008 #3
    I just realized that now, it seems the equations will turn out to be

    mg + un = Fsintheta

    with n = Fcostheta

    eventually F = mg/(sintheta-ucostheta)

    thanks for the heads up.
     
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