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Math Help - Resolving Vectors

  1. #1
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    Resolving Vectors

    Three trucks are trying to pull a fourth truck out of a mud hole. The first truck pulls with 15,000 Newtons straight ahead; the second pulls 18˚ off the right with 18,000 Newtons; and the third pulls 24˚ off to the left with 21,000 Newtons

    a) Calculate the size and direction of the net force exerted by these three trucks

    b) How much more force would be available if the three were hooked together in a straight line?
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    Quote Originally Posted by bigstarz
    Three trucks are trying to pull a fourth truck out of a mud hole. The first truck pulls with 15,000 Newtons straight ahead; the second pulls 18˚ off the right with 18,000 Newtons; and the third pulls 24˚ off to the left with 21,000 Newtons

    a) Calculate the size and direction of the net force exerted by these three trucks

    b) How much more force would be available if the three were hooked together in a straight line?
    Either a diagram or restating the problem in reference to a coordinate axis would be helpful...

    -Dan
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  3. #3
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    Quote Originally Posted by bigstarz
    Three trucks are trying to pull a fourth truck out of a mud hole. The first truck pulls with 15,000 Newtons straight ahead; the second pulls 18˚ off the right with 18,000 Newtons; and the third pulls 24˚ off to the left with 21,000 Newtons
    a) Calculate the size and direction of the net force exerted by these three trucks
    b) How much more force would be available if the three were hooked together in a straight line?
    Hello, bigstarz,

    I've attached a diagram about the situation as I understand it.
    The scale is: 1 length unit is 10 kN.
    So the resulting force (red) is 51.39 kN. The angle between the 1rst truck an the resulting force is 3.3° to the left.

    For your calculation use Cosine rule twice. If I have time and opportunity today I'll show you how to calculate.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Resolving Vectors-trucks1.gif  
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  4. #4
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    Quote Originally Posted by bigstarz
    Three trucks are trying to pull a fourth truck out of a mud hole. The first truck pulls with 15,000 Newtons straight ahead; the second pulls 18˚ off the right with 18,000 Newtons; and the third pulls 24˚ off to the left with 21,000 Newtons
    a) Calculate the size and direction of the net force exerted by these three trucks...
    Hello, bigstarz,

    I calculate first the resulting force of T1 and T2, I call it R_{12}.

    R_{12}=\sqrt{15^2+18^2-2*15*18*\cos(162^\circ)}\approx 32.597\ kN. That's the value (= length) of the blue vector.

    Now you need the value of the angle between T1 and R12. Use Cosine rule again:

    \cos(\alpha)=\frac{18^2-32.597^2-15^2}{-2\cdot 32.597 \cdot 15}\approx 9.826^\circ. So the angle between T3 and R12 is 33.826°.
    The resulting force of all three partial forces T1, T2 and T3 equals the resulting force of R12 and T3. Use Cosine rule again:

    R_{123}=\sqrt{21^2+32.597^2-2*21*32.597*\cos(146.174^\circ)}\approx  51.3896... kN

    to b) Pulling in a straight line the three trucks will provide a total force of 21 kN + 15 kN + 18 kN = 54 kN

    Greetings

    EB
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