physics

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Two tugboats are towing a ship.Each exerts a force of 6000 N and the angle between two ropes is 60 degrees.What is the resultant force on the ship?

  • physics -

    F(net)= 2F•cos30°

  • physics -

    10400

  • physics -

    Fr = 6000[0o] + 6000[60o]
    Fr = 6000 + 3000+5196i = 9000 + 5196i =
    Fr = Sqrt(9000^2 + 5196^2).

  • physics -

    10392 N

  • Physics -

    We need to use law of parallelogram of vector addition. For two vectors

    P
    and

    Q
    having an angle
    θ
    between the two the resultant vector

    R
    is given by




    R



    =





    P



    2
    +




    Q



    2
    +
    2




    P







    Q



    cos
    θ

    and angle of the resultant
    α
    =
    tan

    1









    Q



    sin
    θ




    P



    +




    Q



    cos
    θ





    Inserting given values we get




    R



    =

    (
    6000
    )
    2
    +
    (
    6000
    )
    2
    +
    2
    ×
    6000
    ×
    6000
    ×
    cos
    60






    R



    =

    (
    6000
    )
    2
    +
    (
    6000
    )
    2
    +
    2
    ×
    6000
    ×
    6000
    ×
    0.5






    R



    =
    6000

    3






    R



    =
    10392.3
    N
    rounded to one decimal place.
    and
    α
    =
    tan

    1
    (
    6000
    ×
    sin
    60
    6000
    +
    6000
    cos
    60
    )


    α
    =
    tan

    1




    3
    2
    1
    +
    1
    2





    α
    =
    tan

    1
    (
    1

    3
    )


    α
    =
    30

    measured as per measurement of

    θ

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