A 950-kg car strikes a huge spring at a speed of 25 m/s, compressing the spring 4.0 m. (a) What is the spring stiffness constant of the spring? (b) How long is the car in contact with the spring before bouncing off in the opposite direction?

Question

A 950-kg car strikes a huge spring at a speed of  25 m/s, compressing the spring 4.0 m. (a) What is the spring stiffness constant of the spring? (b) How long is the car in contact with the spring before bouncing off in the opposite direction?

Connor · Accepted Answer

a)
x=4m
m=950kg
v=25m/s

1/2(m)(v)^2=1/2(k)(x)^2
^use this equation to solve for k, should get 37000 N/m

b)
T=2pi*sqrt(m/k)
Use this to solve for T, should get 1s.
T is the time period for the spring to go from equilibrium, to compressed, to stretched, and back to equilibrium. So basically the question is asking for half of T. So your answer should be 0.5s.