A spring with a constant of $4 (kg)/s^2$ is lying on the ground with one end attached to a wall. An object with a mass of $6 kg$ and speed of $3 m/s$ collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2018-04-09T03:53:49

3.7m

Kinetic energy of the object just before hitting the spring:
$E_k=1/2mv^2$
$E_k=1/2*6kg*(3m*s^-1)^2$
$E_k=27J$

Spring potential energy:
$E_e=1/2kx^2$
Where k is the spring constant and x is the spring change in length.

$27J=1/2*4N*m^-1*x^2$
$27/2m^2=x^2$
$sqrt(27/2)m=x$
$3.67...=x$

So the spring will move 3.7m.

A spring with a constant of 4 (kg)/s^24 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 6 kg6 kg and speed of 3 m/s3 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?