- #1

- 25

- 0

## Homework Statement

A 2.14 kg block is dropped from a height of 43.6 cm onto a spring of force constant 18.6 N/cm. Find the maximum distance the spring will be compressed.

I know that the mass is 2.14 kg, the force constant of the spring is K=1860 N/m.

I assume the final velocity, the final height of the block after being dropped, and the final distance the spring will be compressed are 0.

## Homework Equations

U+K=0

v^2=v(0)^2+2AS

## The Attempt at a Solution

To find the initial velocity, I use the constant acceleration equation:

0=V(0)^2-19.7(.436); V(0)=2.92m/s

Since I know (or assume) a conservative force, I use the equation:

U+K=0

mgh+(1/2)mv(0)^2+(1/2)kx^2=0

2.14(-9.8)(.436)-.5(2.14)(2.92)^2+(1/2)(1860)x^2=0

x=.139 m = 13.9 cm

The book got 11.1 cm. Can anyone tell me what I did wrong and how to do the problem correctly? Must help is appreciated. Thanks!