In a ballistic pendulum an object of mass m is fired with aninitial speed (V-0)

Question

In a ballistic pendulum an object of mass m is fired with aninitial speed (V-0) at a pendulum bob. The bob has a mass m, whichis suspended by a rod of length L and negligible mass. After thecollision, the pendulum and object stick together and swing to amaximum angular displacement as shown . Find an expression for V-0, the initial speedof the fired object. Express your answer in terms of someor all of the variables m,M ,L , and and the accelerationdue to gravity, g Initial velocity=????. Find an expression for V-0, the initial speedof the fired object. Express your answer in terms of someor all of the variables m,M ,L , and and the accelerationdue to gravity, g Initial velocity=????.

Explanation / Answer

     From conservation of momentum justbefore and after collision               mv0 = ( m +M )V ----------(1)     Let h is the height reached bythe combained mass then                h = L - Lcos      Apply conservation of energy atbottom of swing and at maxiumum height then             (1/2)mV2 = mg( L - Lcos )                     V = 2g( L - Lcos)                ---------- (2) From equations (1) and (2) we get                     vo = ( m + M)/m [ 2g( L - Lcos ) ]                           

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