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Vector Addition + Extras

  1. Nov 14, 2007 #1
    1. The problem statement, all variables and given/known data

    A 5.0 Kg block at rest on a frictionless surface is acted on by forces F1= 5.5N and F2= 3.5N, as illustrated in the figure.
    A) What additional force (in unit vector notation) is required to keep the block at rest?
    B) What additional force (in unit vector notation) is required to accelerate the block at a rate of 2.25 m/s^2

    Force 1: 3.5N at 37 degrees above +X axis
    Force 2: 5.5N at 30 degrees below +X axis

    2. Relevant equations

    F=m*a
    S O H C A H T O A

    3. The attempt at a solution

    The first step I took was to use trig functions to find the X and Y components of F1 and F2. I came up with the following:

    F1X=3.5cos37=2.80N
    F1Y=3.5sin37=2.12

    F2X=5.5cos30=4.76N
    F2Y=5.5cos30=-2.75N

    Adding the X and Y components from each vector together I came to this answer for "F3" which would represent the two vectors.

    F3X=7.56N F3Y=-0.63N
    Then used Pythagorean theorem to find the hypotenuse (the magnitude of the new force)
    which was:
    7.56^2 + -0.63^2=X^2
    X=7.53N

    To find the angle of the new force I used:

    tan^-1(-0.63 / 7.56) = -4.76 degrees

    This equation gave me essentially the opposite of the angle I was looking for (if I'm thinking correctly about this problem) making the magnitude of the force to "keep the block at rest" would be -7.52N at 4.76 degrees above the -X Axis.


    This answer was turned in and received a 6/10 possible points. I need help determining where I went wrong, and how I can fix it so I can turn the problem back in for a small return...not to mention it's bothering me that I don't know what I did wrong!

    Thanks in advance,

    Ian
     

    Attached Files:

  2. jcsd
  3. Nov 14, 2007 #2
    P.s.

    I think it's possible I received points off for misusing vector notation. How can I express answers in correct unit vector notation?
     
  4. Nov 15, 2007 #3

    andrevdh

    User Avatar
    Homework Helper

    You forgot to include the weight and normal forces acting on the block.
     
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