Measurements and Calculations for Marble Block Collision
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Conservation of Linear Momentum for Marble colliding with a Block
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Before the collision...
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It takes...6frames
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which is...0.00625seconds
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for the marble to travel...0.27meters
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so the velocity is43.2m/s
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the mass of the marble is0.0044kg
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so the linear momentum is (p=mv)0.19008kg m/s
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After the collision (marble)...
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it takes..60frames
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which is0.0625seconds
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for the marble to travel-0.27m
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so the velocity is-4.32m/s
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and the linear momentum is-0.019008kg m/s
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After the collision (block)...
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it takes79frames
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which is 0.08229166667seconds
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for the block to travel0.27m
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so the velocity is3.281012658m/s
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the mass is 0.0645kg
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so the linear momentum is0.2116253165kg m/s
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total momentum after the collision:0.1926173165kg m/s
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total momentum before the collision:0.19008kg m/s
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percent difference1.31728367%
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Key observation: linear momentum is conserved during this collision. The slight increase in momentum is within the range of measurement uncertainty.
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Angular momentum
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marble before the collision...
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the marble is moving43.2m/s
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at a distance from the c.o.m of the block of0.065m/s
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so the angular momentum (l=rmv)0.0123552kg m/s^2
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marble after collision...
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the marble is moving-4.32m/s
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at a distance from the com of the block of0.065m
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so the angular momentum is-0.00123552kg m^2/s
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the block rotating end over end
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it takes79frames
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which is0.08229166667seconds
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the thickness of the block is0.02m
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the length of the block is0.184m
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the rotational inertia is0.000184126kg m^2
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angular momentum of block0.01405850463kg m^2/s
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total angular momentum before collision0.0123552kg m^2/s
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total angular momentum after collision0.01282298463kg m^2/s
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percent difference3.648016745%
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