Hooke's law (Don't know what I am missing)

1. Oct 9, 2009

raiderIV

1. The problem statement, all variables and given/known data
An automobile air bag cushions the force on the driver in a head-on collision by absorbing her energy before she hits the steering wheel. Such a bag can be modeled as an elastic force, similar to that produced by a spring.

Calculate the effective force constant k of the air bag for which the bag will prevent injury to a 65.0kg driver if she is 30.0cm from the steering wheel at the instant of impact.

m = 65 kg
x = .3 meters
F = ?
k = ?

2. Relevant equations
Hooke's Law
F = -kx

F = force
x = displacement(or the distance traveled)
k = the force constant

3. The attempt at a solution
Well I know that this should be an easy solution and I first need to find F, but I do not have a speed that the person is moving. I don't know if I am missing something or if i need to contact the teacher and ask for more information.

Personally I view this as unsolvable without more information, but I just figure that I am missing something.

~John

Last edited: Oct 9, 2009
2. Oct 9, 2009

CFDFEAGURU

You are trying to calculate the value of k, simple solve the equation for k and input in the force (kg) and the distance (cm).

Remember a spring rate has units of kg/m or kg/cm etc ....

Thanks
Matt

3. Oct 9, 2009

RoyalCat

Yes, I think you're right. This can't be solved without knowing the velocity of the driver at the moment of impact.

This can be shown if you choose the velocity of the driver to be an unknown, $$u$$

The cushion absorbs the energy of the driver, find an equation describing this process and solve for $$k$$
It will become immediately apparent that the solution depends on $$u$$

Also, the units of a spring constant are $$\frac{N}{m}$$

4. Oct 9, 2009

raiderIV

I will contact the instructor to see if something was just accidentally omitted.

~John

5. Oct 9, 2009

RoyalCat

The big clue to the fact this problem is unsolvable is that you cannot get a solution from dimensional analysis.

You are given mass, which has dimensions $$[M]$$ and distance, which has dimensions $$[L]$$.

You are asked to find the spring constant, $$k$$, which has dimensions $$[M][L][T]^{-2}[L]^{-1}$$ which is the same as $$[M][T]^{-2}$$

So as you can see, without some known quantity to provide the dimension of time, you cannot get a result, no matter how you arrange your data.

What you should do know, I think, is solve the problem as though $$u$$, the driver's initial velocity, were a known quantity. Just so you have a ready formula to plug the data into once you get word back from your instructor.

An interesting exercise would be to solve using dimensional analysis as well. :)