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March 26, 2017

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A bullet of mass ‘m’ traveling horizontally at a speed ‘v’ embeds itself in the centre of a block of wood of mass ‘M’, which is suspended by a light vertical string of length ‘l’. What would be the maximum inclination of the string with the vertical?

  • physics - ,

    After the bullet gets embedded in the block, the block acquires velocity V given by

    mv = (m+M) V
    V = [m/(m+M)] v

    Then the pendulum swings to a height H while total energy is conserved:

    gH = V^2/2 = [m/(m+M)]^2 v^2/2

    If the maximum inclination angle of the swing is A and the string length is l,

    l (1 - cos A) = H

    Solve for A

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