General Rule for Spring Compression?

[FrenchAtticus]

Though this is part of my homework I posted it here because it's a general rule that applies to all physics and doesn't contain specific values from my homework.

A block of mass m slides on a horizontal frictionless table with an initial speed. It then compresses a spring of force constant k and is brought to rest. How much is the spring compressed x from it's natural length.

*also* Is k the same K as in Force of spring = -Kx

 

[tanker]

(Yes, the k in Hooke's law is lower case).

For this problem you must realize that as the block hits the spring, it moves (covers distance) against the force kx. As a result, the spring does work on the block. Now, how much work it takes to slow the block down as a function of compressed spring distance is essentially what they're asking in this question.

I can't tell you the formula, as that would be doing your homework for you. But...think about how much work the spring does for a small distance assuming the force is constant over that distance - and use that to figure out how much work is done for any compression length x.