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Anonymous
Anonymous asked in Science & MathematicsPhysics · 2 months ago

Collisions in two dimensions. Physics help!?

I dont have any mass , I don’t know how to start !

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  • 2 months ago

    Let the mass of the pucks is m kg and the Puck B velocity after the collision is v m/s at an angle θ from X-axis.

    The initial momentum of pucks on X-axis:

    Puck A: m x 2 = 2m kg-m/s

    Puck B: m x 0 = 0

    The initial momentum of pucks on Y-axis:

    Puck A: m x 0 = 0

    Puck B: m x 0 = 0

    The Final momentum of pucks on X-axis:

    Puck A: m x 1 x cos60* = 0.5m kg-m/s

    Puck B: m x  v  x cosθ  = mvcosθ  kg-m/s 

    The Final momentum of pucks on Y-axis: 

    Puck A: m x 1 x  sin60* = 0.87m kg-m/s

    Puck B: m x v x sinθ = mvsinθ kg-m/s

    BY the law of momentum conservation:

    ON X-AXIS:

    =>m1u1 + m2u2 = m1v1 + m2v2

    =>2m + 0 = 0.5m + mvcosθ

    =>vcosθ = 1.5 --------------------------(i)ON Y-AXIS:

    =>m1u1 + m2u2 = m1v1 + m2v2

    =>0 + 0 = 0.87m + mvsinθ

    =>vsinθ = -0.87 ---------------------(ii)

    BY (ii)/(i):

    =>tanθ = -0.87/1.5 = -0.58 = tan30* (below X-axis)

    =>θ = 30* (below X-axis)

    & By (i)^2 + (ii)^2

    =>v^2 (sin^2θ + cos^2θ) = (1.5)^2 + (0.87)^2

    =>v = √3

    =>v = 1.73 m/s

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  • Joseph
    Lv 7
    2 months ago

    You don't need the mass of the pucks.  They cancel out.  

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  • Ash
    Lv 7
    2 months ago

    Lets say the puck has mass 'm' kg

    Collision in +x-direction

    m(Uax) + m(Ubx) =  m(Vax) + m(Vbx)

    Divide m on both sides

    Uax + Ubx = Vax + Vbx

    2.0 + 0 = 1.0 cos60 + Vbx

    Vbx = 2.0 - 1.0 cos60

    Vbx = 1.5 m/s

    Collision in +y-direction

    m(Uay) + m(Uby) = m(Vay) + m(Vby)

    Divide m on both sides

    Uay + Uby = Vay + Vby

    0 + 0 = 1.0 sin60 + Vby

    Vby = - 1.0 sin60

    Vby = - 0.87 m/s

    speed of puck B = √(Vbx² + Vby²) =  √[(1.5)² + (- 0.87)²] = 1.7 m/s

    direction of puck B = tan⁻¹(Vby/Vbx) =tan⁻¹(- 0.87/1.5) = -30°

    The direction of puck is 30° below +x-direction

    • NCS
      Lv 7
      2 months agoReport

      nice

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