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Motion of a Block with Three Forces

  1. Sep 23, 2007 #1
    The diagram below shows a block of mass m=2.0\; \rm kg on a frictionless horizontal surface, as seen from above. Three forces of magnitudes F_1 = 4.0\;{\rm N}, F_2 = 6.0\;{\rm N}, and F_3 = 8.0\;{\rm N} are applied to the block, initially at rest on the surface, at angles shown on the diagram.

    1. Calculate the magnitude of the total resultant force \vec{F}_{\rm r} = \vec{F}_1+ \vec{F}_2 +\vec{F}_3 acting on the mass.

    2. What angle does F_r_vec make with the positive x axis?

    3. What is the magnitude of the mass's acceleration vector, a_vec?

    4. What is the direction of a_vec? In other words, what angle does this vector make with respect to the positive x axis?

    5. How far (in meters) will the mass move in 5.0 s?

    6. What is the magnitude of the velocity vector of the block at t = 5.0\;{\rm s}?

    7. In what direction is the mass moving at time t = 5.0\;{\rm s}? That is, what angle does the velocity vector make with respect to the positive x axis?


    I just need clarification on how to start this problem...do I simply use Fnet = ma? and to find the resultant im assuming I need the magnitude of vectors forumla, but how do I use it here?

    any help will be greatly appreciated.



    [​IMG]
     
  2. jcsd
  3. Sep 23, 2007 #2

    Doc Al

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    Staff: Mentor

    Sure.
    Just find the components of each force and add them up.
     
  4. Sep 23, 2007 #3

    dlgoff

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    Hint to start with. Break down the forces into their x and y components. Then find the resultant force from these. Rember you'll need to make use of the sin and cos of your angles.
     
  5. Sep 23, 2007 #4
    ok

    so this is what I got:

    f(->)1: 3.63i + 1.69j
    f(->)2: 4.91i - 3.44j
    f(->)3: 8i

    Now to determine the resultant, I just add all of these up?

    I get then f(->)r: 16.54i - 1.75j

    so resultant magnitude is = 16.63 N??
     
    Last edited: Sep 23, 2007
  6. Sep 23, 2007 #5

    Doc Al

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    Add up the components and you have the components of the resultant. (Double check the signs of your components.)
     
  7. Sep 23, 2007 #6
    ok sorry

    the 3rd one has -8i


    So then it should be 1.83 N?
     
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