Anonymous
Anonymous asked in Science & MathematicsPhysics · 3 weeks ago

Mechanics problem: momentum conservation..EMERGENCY!!?

Answer with explanation please :/

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  • 3 weeks ago
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    Part a)

    The total momentum (mass times velocity) is always conserved, but in this case their are 2 momentums, one in the x direction and one in the y.

    Mx = -(1170/9.8)*69 = 8238 kg*m/s left

    My = -(1760/9.8)*49 = 8800 kg*m/s down

    To find the magnitude you use Pythagorean's Theorem because the x and y components form a right triangle.

    Mx^2 + My^2 = Mf^2Mf = 12054 kg*m/s

    Now that you know the final momentum you can divide by the total mass to find the velocity.

    (1170+1760)/9.8 = 299 kg

    Mf/299 = 40.3 m/s 

    Part b)

    To find the direction you will have to use Tan^-1 on the x and y components, so Tan^-1(My/Mx) = angle = 46.9 degrees

    Because the cars are going left and down, the resultant will be in the third quadrent so the angle you got is the angle counter-clockwise from the negative x axis, meaning you will have to add 180 degrees to your answer.

    46.9+180 = 226.9 degrees from East

    • NCS
      Lv 7
      3 weeks agoReport

      Because some people are petty little turds.

  • oubaas
    Lv 7
    3 weeks ago

    Momentum conservation shall apply :

    V = (1170*69+1760*49)/(1170+1760) = 57.0 m/sec

  • Ash
    Lv 7
    3 weeks ago

    m₁ = (1170 / 9.81) kg

    u₁ = 69 m/s in West direction

    m₂ = (1760 / 9.81) kg

    u₂ = 49 m/s in South direction

    v = ?

    momentum conservation in East-West direction

    m₁u₁ + m₂u₂ = (m₁+m₂)v

    v(east-west) = (m₁u₁ + m₂u₂) / (m₁+m₂)

    v(east-west) = ( (1170 / 9.81)69 + (1760 / 9.81) 0) / ((1170 / 9.81)+ (1760 / 9.81))

    v(east-west) =  [(1170*69)/9.81 ] / [(1170 + 1760)/9.81]

    v(east-west) = 80730 / 2930

    v(east-west) =  27.6 m/s

    momentum conservation in North-South direction

    v(north-south) = (m₁u₁ + m₂u₂) / (m₁+m₂) 

    v(north-south) = ( (1170 / 9.81)0 + (1760 / 9.81) 49) / ((1170 / 9.81)+ (1760 / 9.81))

    v(north-south) = 86240 / 2930

    v(north-south) = 29.4 m/s

    Resultant velocity, v = √(27.6² + 29.4²) = 40.3 m/s

    angle S of W = tan⁻¹ (29.4/27.6) = 46.8°

    With respect to East, the angle will be 180°+46.8 = 226.8°

    • Ash
      Lv 7
      3 weeks agoReport

      Thanks Whome for your support. Some guys have been doing it for fun

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