Question

A bullet with mass 25g and initial horizontal velocity 320m=s strikes a block of mass 2kg that rests on a frictionless surface and is attached to one end of a spring. The bullet becomes embedded in the block. The other end of the spring is attached to the wall. The impact compresss the spring a maximum distance of 25cm. After the impact, the block moves in simple harmonic motion.
1. What is the frequency of the oscillation?
2. Sketch graphs for the block's position, velocity, and acceleration as a function of time (x vs. t, v vs. t, a vs. t). Check to make sure your graphs are consistent.
3. Write an description of what is happening to the energy in this system
from the time the bullet is red until the block returns to its starting
position for the rst time. Meaning, tell a story about how the energy
changes form or moves from one object to another.

Answer 1

m=0.025kg, u 025 k9, U= 320mis, m=2K9. d= 0.25 m on conservation of momentum: mu= (m+mv V= mu = 0.025*320 = 3.951 mls. mum 2.025 |V= 3.951 rols.) from conservation of energy Ź (m+m) v² = 1 kd² 5) K= (M+m)v2 = 2.025%(3.951)? = 505.68 N/m (0.25)2 K=505.68 Hlm | A da bo v Sob66 12=2.515 H2 & free. W = 200 = 15.802 rad 8. - angular fresu. mer 2.025

0.25m position vetime - -- -0.25m - Displacement votre 3.951ml + -- - -GS1ml -- - Aceckration time -- Initially, the bloue waid at rest. After Collision system get kinetic Energy, when spring started to compress, Kinetic Energy starts Converting into potential Energy, when Spring is comprased maximum lit, d=0.25m, Kinetic Enersy completely converted into potential Energy.