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Magnitude of vertical force. What am I doing wrong? x_X

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data

    A woman pushes a 20 kg lawnmower at a steady speed. She exerts a 87 N force in a direction of 32 (degrees) below the horizontal. The acceleration of gravity is 9.8 m/s^2. Find the magnitude of the vertical force this lawnmower exerts on the lawn. Answer in units of N.
    • So, mass of lawn mower is 20 kg.
    • She exerts a 87 N force.
    • Force is exerted at 32 degrees.
    • Acceleration of gravity is 9.8 m/s^2.
    • ?magnitude of the vertical force this lawnmower exerts on this lawn?

    2. Relevant equations

    • F=ma
    • Trigonometric: sin(x)

    3. The attempt at a solution

    I first wanted to show you a picture of the problem:

    http://img10.imageshack.us/img10/8034/lawnmowerproblm.jpg [Broken]

    So what I did:

    |\
    |..\
    |.....\ 87N
    |x......\
    |...........\
    |___x_32\

    So I did Sin(32) = x/87
    Sin(32)*87 = x
    X = 46.103, thus which I thought was the downward force exerted.
    Unfortunately it's not.

    What am i doing wrong?!?!!?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 21, 2009 #2
    I think if you are finding the force the lawnmower is exerting on the ground just take mg and add it to the vertical component of the force of the push.

    So mg = (20kg)*(9.8)=196N
    And the vertical component of the force is 87sin(32)=46.1N

    Then just add them together because they are both pointed downward.


    First post!!
     
  4. Oct 21, 2009 #3
    Ah ha! That's what I forgot to do! I forgot to do (20kg)*(9.8)=196N Thanks man!!!! That's exactly right :)
     
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