would someone please help? thanks?

Question

A rifle bullet with mass 8g strikes and embeds itself in a block with mass .992kg that rests on a frictionless, horizontal surface and is attached to a coil spring. the impact compresses the spring 15cm. calibration of the spring shows that a force of .750N is required to compress the spring.250cm.
a) find the magnitude of the block's velocity just after impact.
b) what is the initial speed of the bullet?

Answer 1

We will assume that the spring is linear all the way to 15 cm

F=k*x
k=.75/.25
k=3 N/cm
or
k=300N/m

The collision of the bullet and the block are governed by conservation of momentum

v1*8/1000=v2*1

We know that the compression of the spring is 15 cm. Using conservation of energy

.5*1*v2^2=.5*k*.15^2
v2=.15*sqrt(300)
V2= 2.6 m/s

This is the speed of the block after collision

The speed of the bullet is
2.6*1000/8
=325 m/s

j