A safe held by a string breaks and lands on a spring

[talaroue]

Homework Statement

A 1209 kg safe is 1.54 m above a heavy-duty spring when the rope holding the safe breaks. Thr safe hits the spring and compress it 53 cm. What is he spring constant of the spring?

Homework Equations

K=mV^2/2
U=mgh
Ki+Ui=Kf+Uf

The Attempt at a Solution

I thought I understood momentuem and energy but not anymore. Here is what I did...

Ui=mgh= 2*9.8*1.54
Kf=mV^2/2

Then solved for V and got 5.494 m/s

Then used that velocity for the spring constant by using...

U=k(delta x)^2/2
K=mV^2/2

then solved for k and got 129912 N/m... but that is coming up wrong what am i doing wrong.

 

[talaroue]

any ideas?

 

[PhanthomJay]

Well for one thing you are using m = 2 kg when it is given that m = 1209 kg. Then you neglect the gravitational potential energy in the 2nd set of equations. It is better to do this all in one step: Initial energy = Final energy, where v_initial = v_final = 0.

 

[tiny-tim]

Hi talaroue!

(try using the X² and X₂ tags just above the Reply box )

A 1209 kg safe is 1.54 m above a heavy-duty spring when the rope holding the safe breaks. Thr safe hits the spring and compress it 53 cm.
…
Ui=mgh= 2*9.8*1.54

No, the safe stops moving 53cm lower.

 

[talaroue]

JAY:

so your saying that i should just use U=mgh and U=k(delta x)^2/2...solve for k and get...

k=2mgh/delta x^2

TINY TIM:

so I didn't go about the problem wrong I just have to add the .53 m to the hieght?

 

[Astronuc]

The safe starts 1.54 m (154 cm) above the spring and then travels another 0.53 m after contact. That must be considered with respect to gravitational potential energy.

 

[PhanthomJay]

JAMES:

so your saying that i should just use U=mgh and U=k(delta x)^2/2...solve for k and get...

k=2mgh/delta x^2

Yes, but 'h' is as noted by others, and don't forget to correct your value of 'm'.

 

[talaroue]

ahhh I see at least I had the right idea just need to be more careful. If you guys don't mind I am having problems with another problem as well... it might be a same problem i am going to go back and look at it but I made a thread about it as well...

https://www.physicsforums.com/showthread.php?t=316282"

 

[talaroue]

Yes, but 'h' is as noted by others, and don't forget to correct your value of 'm'.

I wasn't using 2 as my m, that was just noting the second equation is U=k(delta x^2)/2 I didn't combined them when i posted that, i see what you are saying though.