Question

An object is attached to a vertical spring and slowly lowered to its equilibrium position. This stretches the spring by an amount d. If the same object is attached to the same vertical spring but permitted to fall instead, through what maximum distance does it stretch the spring?

Answer 1

h=2d

Step-by-step explanation:

As is known, in equilibrium position,

`F=m*g=K*d`

The position maximum spring stretch after the mass is dropped so:

`m*g*(d+y)=(1)/(2)*K*(d+y)^2`

Since (d+y)>0

`m*g=(1)/(2)*K*(d+y)`

`2*m*g=K*(d+y)`

K=m*g with out friction

`2*K*d=k*(d+y)`

`2*d=(d+y)`

h=(d+y) so :

The maximum distance is h=2d