Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Shah asked in Science & MathematicsPhysics · 2 months ago

Mechanics- forces in two dimensions ?

A ship of mass 10000 kg is being towed due north by two tugboats with acceleration 0.1m/s^2. One pulls with a tension of 2000N on a bearing of 330 degree. The other pulls with a tension, T on a bearing of theta. There is resistance against the motion of 1000 N. Find T and theta.

4 Answers

Relevance
  • 2 months ago
    Favorite Answer

    The applied force is (ma + 1000N) northward,

    which is 2000N northward.

    So you have 

    (2000 N)(-i/2 + j*sqrt(3)/2) + T(i sin(theta) + j cos(theta)) =

    = (2000 N) j.

    Hence,

    T*sin(theta) = 1000 N and

    T*cos(theta) = 2000 N - 1732 N = 268 N.

    Then tan(theta) = 1000/268 = 3.731 and theta = 75 degrees, and T = 1035 N. 

  • oubaas
    Lv 7
    2 months ago

    T1 = 2000 N

    T1x = 2000*cos 30 = 1730 N

    T1y = -2000*sin 30° = -1000 N 

    Tx = -T1x = -1730 N

    Ty = -T1y + Fattr. + m*a = 1000+1000+10.000*0.1 = 3000 N 

    T = Tx^2+Ty^2 = 

    T = √((√3)/2)^2*2000+3000^2 = 1000√3/4*2^2+3^2 = 1000√3+9 = 2000√3 N 

    bearing angle Θ = 180+arctan  -Tx/Ty = 180+arctan (√3)/3 = 180+30 = 210°

  • 2 months ago

    330º is 30º west of N.

    The N component is 2000cos30 = 1732 N

    The W component is 2000sin30 = 1000 N

    net N force on the ship is sum of

    F = ma = 10000•0.1 = 1000 N

    added to 1000 N resistance = 2000 N

    It is all N, no W or E component

    net W or E force is zero

    so N component of second tug is 2000–1732 = 268 N

    and W component = –1000 N or E force of 1000 N

    vector sum of the two is √(1000²+268²) = 1035 N

    angle θ = arctan (268/1000) = 15.0º which would be, looking at the vectors, 75º E of N

  • Anonymous
    2 months ago

    North = 90° or 0° or 270°? THINK

Still have questions? Get your answers by asking now.