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

## 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?

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.

any ideas?

PhanthomJay
Homework Helper
Gold Member
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
Homework Helper
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. 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?

Last edited:
Astronuc
Staff Emeritus
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
Homework Helper
Gold Member
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'.

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....