Looking for some help on my physics homework?

Question

What should be the spring constant k of a spring designed to bring a 1200 kg car to rest from a speed of 109 km/h so that the occupants undergo a maximum acceleration of 5.0 g?

Answer 1

The maximum acceleration will be the instant before the car comes to a stop because that is when the spring will have maximum force.

this gives you the equation
F=K*x=m*a
K*x=1200*5*9.81

Then you can set up another equation where you solve for when the car comes to a stop using conservation of energy:

.5*m*v^2=.5*m*K*x^2
v^2=K*x^2
(109*1000/3600)^2=K*x^2

now you have two simultaneous equations and two unknowns K and X. I would solve for x first and use the positive root (it is a quadratic). Then solve for K.

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