Spring Constant and Potential Energy

[cdm1a23]

Hi,
I am trying to figure out a question in first semester physics... I have a different but similar question that I have the answer for that I am trying to work to figure out the process for the other question.
What is the spring constant k of a spring designed to stop a 1300 kg car traveling 90 km/h so that the occupants experience a maximum acceleration of 5 g? (no friction or other forces mentioned)
I am getting an answer that is about 4 times larger than the given answer of 5 x 10^3 N/m
Here is what I did:
-Changed 90 km/h to 25 m/s
-Calculated 5g as 49 m/s/s
-set 1/2kx^2 = 1/2mv^2 --> KE = Potential Elastic Energy
-found x to be 6.378m because an acceleration of 49m/s/s should stop a car going 25 m/s in 6.378m
- used above numbers in above equation to get 19973.5076?
Does anyone know what I did wrong? Was it a math mistake or should I not be solving for x in that way?
Thanks Very Much

 

[Päällikkö]

You calculated it as if 5g was the average acceleration. It's the maximum acceleration. When do the occupants experience the maximum acceleration?

 

[cdm1a23]

Hmmm,

Thanks very much for the fast response Päällikkö!

I guess the max acceleration would be when the spring was at its most compressed... I think this is leading to calculus... so if the max accel would be at its most compressed, I am not sure how to approach this question at this point...

I am good at math, but not as good at figuring out how to apply the calculus to the problems

 

[Päällikkö]

Thanks very much for the fast response Päällikkö!

No problem .

Hooke's law:
F = -kx
Newton II:
F = maYou shouldn't need calculus here.

Don't get frustrated, I'm trying to give minimal hints, just something to grasp onto. This way the pleasure of finding things out will be maximal, and you'll learn better by trying it out yourself first.
Solving the problem does require thinking from the physics point of view. Do ask for more assistance if you find it insufficient.

 

[cdm1a23]

I might just be brain dead from doing different types of problems all day, but I still don't quite see what I am supposed to do... I had those two equations also, but we have been doing PE and KE recently and I think I am supposed to use that somehow?

I can't figure out how I would calculate the max acceleration of the spring without knowing the spring constant or the distance moved by the spring...

Thanks again for helping. I actually have to run to class, but I will be back in a couple hours, so thanks to anyone else who responds in the meantime.

 

[Päällikkö]

This is quite a lot of help, select the text to see it (I've painted it in white, so I wouldn't spoil the problem ). Don't rush things though, before peeking at what I've written, give the problem a thought, in peace. You can't really concentrate if you have to run for class.

1/2kx² = 1/2mv²
F = -kx
F = m(-5g)

It's down to mathematics now.

With this info, can you solve for k?

 

[cdm1a23]

Got it!

Hi Päällikkö,

I finally figured it out! I guess I just didn't realize that I had enough info in front of me already!

Thanks very much for helping me get to the answer.