PHYS171_f11_lecture_supp_33

# PHYS171_f11_lecture_supp_33 - Multi-state collision problem...

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Multi-state collision problem. ALP November 4, 2011 A bullet of mass m = 5 g is fired at 400 m / s and hits a block of mass M = 1 kg attached to a spring and passes through the block, exiting the other side. Afterwards the block moves, compressing the spring by a distance L = 5 cm . The spring constant is k = 900 N / m . How fast is the bullet moving when it exits the block? In the first part of the problem (the collision) the bullet passes through the mass, depositing some momentum and some kinetic energy but not all, since it comes out the other side and continues moving. In the second part of the problem the resulting motion of the block compresses the spring. In the first part of the problem we cannot apply energy conservation, since an un- known amount of energy was dissipated as the bullet passes through the block (making a hole in it). However momentum is conserved since momentum the only forces in- volved are between the two objects in our system, the bullet and the mass. (We have v 0 M (a) v e M (b) (c) M v b

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