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

[Jshua Monkoe]

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?

 

[Nebozilla]

You do know k. F=kx. I am sure with k you know all you need with conservation of energy.

 

[kerimek]

Great job on using the conservation of energy principle to solve for the velocity of the system after impact. To find the initial speed of the bullet, we can use the same principle and equate the initial kinetic energy of the bullet to the work done by the spring. The equation would be 1/2mv^2 = 1/2kx^2. Since you know the mass of the bullet and the spring constant (k) can be calculated using the given force and compression values, you can solve for the initial speed of the bullet. Keep in mind that the initial speed of the bullet would be much greater than the velocity of the system after impact, since the bullet is much lighter and has a higher velocity than the block.