Answer:
Simple springs obey Hooke's Law. Hooke's Law states that the force on a spring is proportional to it's displacement from it's resting length:
F = -k*x
Where F is the force, x is how far the string is stretched or compressed, and k is a proportionality constant called the spring constant. The negative sign is because the spring resists stretching.
In this case, we can solve for k using the first case:
(100N) = -k * (5cm)
k = ???
And plug that answer in to find x in the second case:
(360N) = -k * x
This is a "Hooke's Law" problem: the restoring force required to compress or stretch a spring is proportional to the distance the spring is deformed. You can figure solve it by setting up a proportion equation and then using the algebraic tool of cross multiplication to solve for the unkown "stretch".
1) set up the proportion equation
100 = 360
5 x
2) cross multiply to get a linear equation
100x = 5*360
3) solve for x
100x = 1800
x = 18
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