Finding the Stopping Point of a Falling Mass on a Spring

[zachmgilbert]

Homework Statement

A 0.25 kg mass is attached to a spring with spring constant 5.4 N/m and let fall. To the nearest hundredth of a meter what is the point where it 'stops'?

diagram here:
http://wps.prenhall.com/wps/media/objects/1088/1114633/ch11/grav.gif

Homework Equations

y=Asin(k/m)^1/2t

The Attempt at a Solution

I don't know how to find t, or I am using the wrong equation.

 

[Winzer]

What is going on(Force wise) when the mass reaches its lowest point?

 

[zachmgilbert]

I tried F=-kx using mg for force. mg is (.25)(9.8) which equals 2.45. Dividing by 5.4 gave me .45 which is wrong. The correct answer is .91

 

[zachmgilbert]

It is a giancoli problem so I can reset the variables. I've tried it multiples times and the F=-kx is always half of the correct answer. Where does it get multiplied by 2.

 

[PhanthomJay]

Your equation assumes the weight is slowly lowered to its equilibrium position. In this case, however, it is dropped suddenly. Use conservation of energy to show that its total stretch is twice the stretch in its at rest equilibrium position.

 

[zachmgilbert]

i have .5mv²=.5kx² but i don't know how to find velocity.

 

[PhanthomJay]

i have .5mv²=.5kx² but i don't know how to find velocity.

The object starts from rest with no speed, and when it reaches the bottom, it momentarily stops and also has no speed. But there is gravitational potential energy at the top, and spring potential energy at the bottom.

 

[zachmgilbert]

Thank You, that gave me the right answer.