Finding the spring constant of a accident safety system

AI Thread Summary
To find the spring constant of an accident safety system designed to stop a 1000 kg vehicle moving at 5 m/s in 0.5 m, the force of the collision must be calculated. The user attempted to find the acceleration using the kinematics equation, resulting in an acceleration of 25 m/s², which is correct in magnitude but should be negative due to deceleration. The discussion confirms that the acceleration should indeed be negative, indicating a reduction in speed. This negative acceleration is crucial for calculating the force and subsequently the spring constant using the formula F = kx. Understanding these dynamics is essential for designing effective safety systems.
Revan718
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Homework Statement


An accident safety system uses a spring to absorb the energy of a car before the car collides with a bridge abutment.
The vehicle has a mass of 1000kg and the design calls for stopping a car moving at 5m/sec (11.2 mi/hr) in 0.5m.
Find the spring constant k


Homework Equations


F=kx -> k=F/x


The Attempt at a Solution


I am having trouble finding the force of the collision. It is needed to find k, is it not? I was thinking I may need to use a kinematics equation to do this and solve for the acceleration (deceleration in this case).
 
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I tried using the equation:
v^2=v(0)^2+2a(s-s(0))
and solved for a, resulting in a=25m/s^2
Is this correct?
 
Revan718 said:
I tried using the equation:
v^2=v(0)^2+2a(s-s(0))
and solved for a, resulting in a=25m/s^2
Is this correct?

Shouldn't the acceleration be negative?
 
Nice work, Revan718. Acceleration is negative.
 

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