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Calculate acceleration of object with applied force and friction

  1. Jun 13, 2009 #1
    1. The problem statement, all variables and given/known data

    A worker drags a crate across a factoryt floor by pulling on a rope tied to the crate. The worker exerts a force of 450 N on the rope, which is inclined 38 degrees to the horizontal, and the floor exerts a horizontal frictional force on 125 N that opposes the motion. You can assume the crate doesn't leave the ground.

    Calculate the acceleration of the crate (mass = 310 kg).

    2. Relevant equations

    F = ma

    3. The attempt at a solution

    Broke the force of the pull into x and y components:

    Fx = 450 cos 38 = 354 N
    Fy = 450 sin 38 = 227 N

    Then the friction opposes motion, so subtract that from the x component

    Fx = 354 - 125 = 229 N

    so the net force is [tex]\sqrt{229^2 + 227^2}[/tex] = 322 N

    then, [tex]a = \frac{F}{m} = \frac{322}{310} = 1.0 ms^{-2}[/tex] to 2 s.f.

    However the answer given is 0.74 ms
     
  2. jcsd
  3. Jun 13, 2009 #2

    Cyosis

    User Avatar
    Homework Helper

    You're doing well until

    The crate does not leave the ground so the only acceleration will be in the x-direction.
     
  4. Jun 13, 2009 #3
    Ah, got it...

    [tex] a = \frac{F_x}{m} = \frac{229}{310} = 0.74 [/tex]

    Thanks.
     
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