Finding a landing speed from spring constants

[euphtone06]

Homework Statement

Problem: http://img147.imageshack.us/img147/8509/physjc9.gif
Additional info: mass of the lander 7750 kg, 1.790967742 is the mag of acceleration due to gravity, this info was found in earlier parts of the problem

Homework Equations

I used these 2 equations and set them equal
[1/2(kx^2)] * 3 = 1/2mv^2

The Attempt at a Solution

[1/2(11566.7)1.2^2] * 3 = 1/2(7750)v^2
solve for v, v= 2.53919 m/s, which was wrong
is the equation wrong?

 

[Ja4Coltrane]

Well, as the spring compresses, there is an aditional energy which must be compensated for.

 

[euphtone06]

And how might I find this additional energy and apply it to the problem at hand?

 

[D H]

You have forgotten the weight of the vehicle. At the point of maximum compression, the springs have fully absorbed the vehicle's kinetic energy just prior to contact and are supporting the vehicle's weight.

 

[euphtone06]

How do I apply the weight to the equation?

 

[D H]

The vehicle will bounce a bit and eventually come to a rest with the springs compressed to balance the force due to gravity. What is the final compression of the springs?

 

[euphtone06]

.4 m?
(7750*1.790967742)/ (3 * 11566.7 ) = .3999988473

 

[D H]

A further hint: It is the compression relative to the final compression (weight on springs) as opposed to the compression relative to the relaxed length you need to use in determining the kinetic energy absorbed by the springs.

 

[euphtone06]

Im completely lost. The weight on springs is 13880 N and uncompressed length is 2.4 compressed is still 1.2 which is stated in the problem.

 

[D H]

You already know that using an uncompressed length of 2.4 meters gives the wrong answer. (BTW, what is the right answer and how do you know it?) That suggests you are using the wrong uncompressed length. The vehicle will eventually come to rest with the springs slightly compressed by the weight of the vehicle. Any length other than this final compression state represents energy (e.g. landing kinetic energy) put into the springs.