Question

simple way to measure the speed of a bullet is with a ballistic pendulum, which consists of a wooden block of mass m into which a bullet of mass m, is shot. The block is suspended from two cables, each of length L. Assume that the time the bullet takes to come to rest (that is, the bullet is moving at the same speed as the block) is negligibly Small. The impact of the bullet causes the block and embedded bullet to swing through a maximum angle . The initial speed of the bullet is vo- mit m , L. 8. a) Find a relation for the initial speed of the bullet as a function of m and o b) How much mechanical energy is lost due to the collision?

Answer 1

hp = L – L cos 0 = L(1 – coso) a) Conservation of momentum, Pinitial = Pfinal m2ū0 + 0 = (mi + m2) v = v= mlo mi + m2 Conservation of energy, Kinetic energy immediately after the collision = Potential energy when the pendulum reaches maximum deflection (m + m2)u2 = (mı + m2)gL(1 – cosø) → v= V2gL(1 - cosº) m20o = 29(1 – cos 4) + vo = (1 + m.) V29(1 – cos ø) mi + m2 T112

o = (mı + m2)gL(1 - cos 0)+H 121 25L(1 - cos 0) = (mi + m2) L(1 - cos 0) + H m2 . H= –(mž + 2m1m2 + m{gL(1 – cos o) - (mı + m2)gL(1 - cos ) m2 H = 914 –cos) [me + 2m + i - (m + ms] H = m (1 + m) 94(1 – cos 6)