Please show all steps having trouble! Thank you A 5.0-gram bullet moving with an

Question

Please show all steps having trouble! Thank you A 5.0-gram bullet moving with an initial speed of 500 m/s is fired into and passes through a 1.0-kg block, as in the figure. The block, initially at rest on a frictionless horizontal surface, is connected to a spring. The spring is not compressed, and the block is moving, as the bullet leaves the block. If the block moves a maximum of 7.0 cm to the right after impact, and takes 0.1 seconds to return to its equilibrium point, find Find the speed at which the bullet emerges from the block. Find the mechanical energy lost in the collision.

Explanation / Answer

a) Here, 0.2 = 2pi * sqrt(1/k)

=> spring contant = 985.96 N/m

Thus, 1/2 * 5 * 10-3 * 500 * 500 = 1/2 * 985.96 * 0.07 * 0.07 + 1/2 * 5 * 10-3 * v2

=> speed of bullet , v = 499 m/s

b) mechanical energy lost = 1/2 * 985.96 * 0.07 * 0.07

                                           = 2.415 J

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