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jaded18
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In a ballistic pendulum an object of mass m is fired with an initial speed v_0 at a pendulum bob. The bob has a mass M, which is suspended by a rod of length L and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement theta as shown http://session.masteringphysics.com/problemAsset/1010989/26/1010989A.jpg
Find an expression for v_0, the initial speed of the fired object.
Express your answer in terms of some or all of the variables m, M, L, and theta and the acceleration due to gravity, g.
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i know that there are two events. the first one is the inelastic collision, where momentum is conserved and mv = (m+M)(V) ... and V = mv/(m+M) ... and when the block swings up mechanical energy is conserved so that (K initial + U initial) = (K final + U final) and (0.5(m+M)V^2) = (m+M)g(h) ... and the bullet speed is ((m+M)/m)(sqrt 2gh) ... how do i incorporate this theta variable that the problem is asking for?
i am so confused!
Find an expression for v_0, the initial speed of the fired object.
Express your answer in terms of some or all of the variables m, M, L, and theta and the acceleration due to gravity, g.
_____
i know that there are two events. the first one is the inelastic collision, where momentum is conserved and mv = (m+M)(V) ... and V = mv/(m+M) ... and when the block swings up mechanical energy is conserved so that (K initial + U initial) = (K final + U final) and (0.5(m+M)V^2) = (m+M)g(h) ... and the bullet speed is ((m+M)/m)(sqrt 2gh) ... how do i incorporate this theta variable that the problem is asking for?
i am so confused!
no prob!