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Math Help - Force vectors

  1. #1
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    Exclamation I don't understand!

    A 1.5-kg object moves up the y-axis at a constant speed. When it reaches the origin, the forces F1 = 5.0 N at 37o above the +x-axis, F2 = 2.5 N in the +x-direction, F3 = 3.5 N at 45o below the -x-axis, and F4 = 1.5 N in the -y-direction are applied to it. (a) Will the object continue to move along the y-axis? (b) If not, what simultaneously applied force will keep it moving along the y-axis at a constant speed?
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  2. #2
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    Well, add up all the forces (using vector addition) to find out what the net force is acting on the object, call it \Sigma F.

    i.e. \Sigma F = F_1 + F_2 + F_3 + F_4.

    For part (a), if the angle of \Sigma F is along the y-axis, or if its magnitude is zero, then the object will stay on the y-axis.

    For part (b), apply a force of the same magnitude but opposite direction (that is, apply -\Sigma F) to allow the object to continue along the y-axis at its original speed.
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  3. #3
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    Quote Originally Posted by Celia
    A 1.5-kg object moves up the y-axis at a constant speed. When it reaches the origin, the forces F1 = 5.0 N at 37o above the +x-axis, F2 = 2.5 N in the +x-direction, F3 = 3.5 N at 45o below the -x-axis, and F4 = 1.5 N in the -y-direction are applied to it. (a) Will the object continue to move along the y-axis? (b) If not, what simultaneously applied force will keep it moving along the y-axis at a constant speed?
    Hello,

    I've attached a diagram to clarify(?) the situation described by your problem.

    to a) The blue vectors are

    \overrightarrow{\overrightarrow{F_1}+ \overrightarrow{F_2} }\ \mbox{and}\ \overrightarrow{\overrightarrow{F_3}+ \overrightarrow{F_4} }

    then I added these vectors and got the result (=red vector). It has a value of 4.133 N and forms an angle of -13.5 with the x-axis.

    to b) the object will move on undisturbed if all applied forces have the value 0. So applie a force \overrightarrow{F_5} which has the value of the red resulting vector and points in the opposite direction.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Force vectors-vierkraft.gif  
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