I am doing a ballistic pendulum lab where i shot a dart out of an air gun at a w

Question

I am doing a ballistic pendulum lab where i shot a dart out of an air gun at a wooden block hung from two strings and measured how much the block moved upon impact with the dart. I need to use the conservation of linear momentum to write an equation for the collision between the dart and the target (from just before to just after the collision.) Also an equation for the motion right AFTER the collision (as the target and dart move up and back). DONT PLUG IN NUMBERS. Why can we use the conservation of linear momentum for this collision? and what type of collision is this and why? Sorry for the long problem guys but its literally all part of one lab question.

Explanation / Answer

The collision between the ball and the pendulum is perfectly inelastic because the ball is embedded in the pendulum after the collision. Conservation of momentum allows us to relate the initial momentum of the system to the nal momentum of the system, change in p = 0; (10.1) pi = pf : (10.2) If m is the mass of the ball, M is the mass of the pendulum, v0 is the initial velocity of the ball, VB is the initial velocity of the pendulum, and V is the nal velocity of the ball and the pendulum, the momentums may be written as, mv0 + MVB = mV + MV: (10.3) Since the pendulum is initially at rest, VB = 0. Solving for the initial velocity of the ball we nd, mv0 = (m + M)V; (10.4) v0 = (m + M)*V/m: (10.5)

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