Spring is compressed x=-D by an object then the object stops at a distance of 3D when released. If spring is compressed by x=-2D what distance will it reach now

Question

An object is on a flat surface. Why is it not 6D? Any help would be appreciated!

 

full question: An object is on a flat surface. If a spring is compressed x= -D by the object, then the object stops at a distance of 3D when released. If the spring is compressed by x= -2D, then what distance will it reach (in terms of D)? Why is it not 6D?

Answer 1

If I am interpreting the information correctly, all of the potential energy of the compressed spring is lost to friction, which brings the block to rest.  I suggest equating the elastic potential energy of the compressed spring to the absolute value of the work done by friction, and use that to find the final distance in the second case.

 

f = force of friction, which I assume is a constant (μmg)

d = distance traveled under friction

 

When compressed by -D:

 

kx²/2 = fd

 

k(-D)²/2 = f(3D) 

 

kD²/2 = 3fD

 

kD/2 = 3f

 

f = kD/6

 

Now use this f to calculate a new d' for the spring compressed by -2D.

 

k(-2D)²/2 = fd' = (kD/6)d'

 

k(4D²)/2 = (kD/6)d'

 

2D = d'/6

 

d' = 12D

 

So I get that it should be 12D.  Were you given an answer to check your result?