A 10.0 g bullet is fired into and embeds itself in a1.75 kg block attached to a

Question

A 10.0 g bullet is fired into and embeds itself in a1.75 kg block attached to a springwith a spring constant of 23.0 N/m andwhose mass is negligible. How far is the spring compressed if thebullet has a speed of 300 m/s just before it strikes the block, andthe block slides on a frictionless surface? (Note: Youmust use conservation of momentum in this problem.) Please Help, I got the answer of 0.361 but this is incorrectand don't know what else to try. A 10.0 g bullet is fired into and embeds itself in a1.75 kg block attached to a springwith a spring constant of 23.0 N/m andwhose mass is negligible. How far is the spring compressed if thebullet has a speed of 300 m/s just before it strikes the block, andthe block slides on a frictionless surface? (Note: Youmust use conservation of momentum in this problem.) Please Help, I got the answer of 0.361 but this is incorrectand don't know what else to try.

Explanation / Answer

    Mass of the bullet, m = 0.01 kg     Mass of the block, M = 1.75 kg     Velocity of the bullet before striking theblock, V = 300 m/s     Velocity of the bullet +block after striking theblock = V '     Spring constant, K = 23 N/m     From law of conservation of momentum,     Momentum of bullet + block after collision =Momentum of bullet before collision     ( m + M ) V ' = m V     1.76 V ' = 0.01 * 300     V ' = 1.7 m/s     Potential energy of spring = Kinetic energy ofbullet + block     ( 1/2 ) K x 2 = ( 1/2 ) ( m + M ) V '2                K x 2 = ( m + M ) V ' 2                     23 * x 2 = 1.76 * 1.7 2     Compression of the spring, x = 0.472 m

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