How Fast Does the Block Move After the Bullet Embeds?

AI Thread Summary
The discussion revolves around a physics problem involving a bullet embedding into a block and compressing a spring. The user initially struggles with applying the conservation of momentum and energy principles to find the block's velocity after impact. They mention using dimensional analysis to derive a force and work done on the spring, but their calculations lead to discrepancies with the expected solution. Ultimately, they realize that knowing the spring constant simplifies the problem significantly. The key takeaway is that understanding the spring's properties is crucial for accurately solving the velocity of the block post-impact.
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Homework Statement


A rifle bullet of mass 7.2 grams strikes and embeds itself in a block with mass 0.819 kg that rests on a frictionless horizontal surface and is attached to a coil spring. The impact compresses the spring 17 centimeters. Calibration of the spring shows that a force of 0.68 Newtons is required to compress the spring 0.31 cm. Find the magnitude of the block’s velocity just after impact. Give your answer in m/s to the first decimal place.


Homework Equations





The Attempt at a Solution


I have looked at at least 4 other posts on this forum about this question, but I still cannot quite get it.

m1v1 = (m1+m2)v2

Using some dimensional analysis, I get that force is equal to some 37 N. Multiply this with the 17 cm, and you get the work done on the spring. This is equal to .5 * m * v1^2. Solve this for V1, plug back into the momentum equation to get V2. Is this not correct because my answer differs from the solution.
 
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Ok, so I finally found the solution, and it's something pretty stupid that I never thought of. k the spring constant is given, then everything else is simple.
 
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