How Do You Calculate the Initial Speed of a Bullet After It Embeds in a Block?

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SUMMARY

The discussion focuses on calculating the initial speed of a bullet after it embeds in a block using principles of conservation of momentum and energy. The bullet has a mass of 8.00g and strikes a block of mass 0.992kg, compressing a spring by 15.0cm. The spring constant is derived from the force required to compress the spring, which is 0.750N for 0.250cm, resulting in a spring constant (k) of 12.00 N/m. The block's velocity just after impact is calculated to be approximately 26.83 m/s, leading to the determination of the bullet's initial speed through energy conservation methods.

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Homework Statement



A rifle bullet with mass 8.00g strikes and embeds itself in a block with mass 0.992kg that rests on a frictionless, horizontal surface and is attached to a coil spring. The impact compresses the spring 15.0cm. The callibration of the spring shows that a force of 0.750N is required to compress the spring 0.250cm.
(a) find the magnitude of the block's velocity just after impact.
(b) what is the initial speed of the bullet?

Homework Equations


mass(bullet)=8.00g
mass(block)=0.992g
compression=15.0cm
1/2mu^2+1/2mv^2 = KE
Work done(spring)= 1/2kx^2

The Attempt at a Solution



(a) I tried 1/2mv^2=KE(SINCE u=0)
I then got v~26.83
(b) I guess the best attempt is of using the law of conservation of energy relating KE to the Work done(spring)
i am not sure of this trial because i don't know k, also is it wise for me to look at the initial velocity of the system as large?
 
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You do know k. F=kx. I am sure with k you know all you need with conservation of energy.
 

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