Physics bullet spring

Question

A 20.0 g bullet traveling at 259 m/s is fired into a 0.411 kg wooden block anchored to a 101 N/m spring. How far is the spring compressed?

 

If the speed of the bullet is not known but it is observed that the spring is compressed 53.9 cm, what was the speed of the bullet?

Answer 1

Momentum of bullet = mass * velocity = 20* 10 ^{- 3} *259 

Momentum of Bullet plus wooden block

= Total mass * Combined velocity

( 411 +20) * 10 ^-3 V

Equating the Momentum before and after 

Find the Value of V

 

Let X = compression of the spring

The PE of spring = KE of Block plus bullet combined

1/2 K *X ² =1/2 ( 431* 10 ^-3 ) V ^{2 :}Find the value of X using K = 101 N/m