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

talaroue

1. The problem statement, all variables and given/known data
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?


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


3. 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 )
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

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....

Second problem I have issues with

talaroue

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.