Hanging Mass on Connected Springs · Physics Brawl 2019 #FoL.23

Physics · mechanics

Problem

Two springs with identical length

l = 5.0

m and stiffness

k = 1.0 \cdot 10^5

N·m⁻¹ are stretched horizontally between two vertical walls (at the distance

2l

) in such a way that the springs are connected in the middle. Next, we hang a mass

m = 3.0

kg at the point where the springs are connected. What is the height

h

by which the point of connection drops? You may assume that

h \ll l

and

g = 9.81

m·s⁻².