a) A wooden block of mass M = 2.64 kg is rest on a frictionless, horizontal tabl

Question

a) A wooden block of mass M = 2.64 kg is rest on a frictionless, horizontal table attached to the end of an unstretched spring (k = 237 N/m). A bullet of mass m = 8.51 g is fired horizontally into the block at speed vo = 354 m/s. The bullet comes to rest inside the block, and causes the mass to oscillate on the spring. If there is no friction between the block and the table: find A, the amplitude of the resulting oscillation. You can assume the mass never hits the wall (to which the spring is attached.)
1 m

b) Two children are playing a game in which they attempt to hit a small box on the floor using a spring-loaded marble gun fastened on the edge of a frictionless, horizontal table. The box is d = 1.37 m from the base of the table, and the marble is fired horizontally. The first child compresses the spring distance x1 = 3.1 cm, and the marble falls short by ?d1 = 26.7 cm. Find x2, the distance the second child should compress the spring so the same marble falls into the box.
2 cm

Explanation / Answer

a) Energy of incoming bullet = (1/2) * (8.51/1000) * (354)2 J = 533.22 J

Energy at amplitutde = (1/2) * k * A2

Hence, A = (533.22*2/237) = 2.12 m

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