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AP® Physics C: Mechanics

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Momentum and Collisions: Final Speed of Spring Loaded Blocks

APPHMC-KK9TP9

Figure 1. Cinsy Krehbiel. Created for Albert.io. Copyright 2016. All rights reserved.

Two blocks are at rest on a frictionless surface. The smaller block has a mass of $m$; the larger block has a mass of $3m$.

An ideal spring, with a spring constant of $k$, is sandwiched between them. As shown in Figure 1, the spring is compressed by $x$. The blocks are released and allowed to slide apart.

Determine the final speed of the heavier block in terms of $m$, $k$, $x$, and any constants.

A

$v=\cfrac{3kx^2}{m}$

B

$v=\sqrt{ \cfrac{3}{m}}\text { }kx$

C

$v=\sqrt{ \cfrac{kx^2}{2m}}$

D

$v=\sqrt{ \cfrac{kx^2}{9m}}$

E

$v=\sqrt{ \cfrac{kx^2}{12m}}$