What is the total distance traveled by the mass on a compressed spring?

[Jinzui]

Homework Statement

A horizontal k=200N/m spring is compressed 80cm. A 10kg mass is palced at the of of the spring on a u(mew)=0.15 surface. The mass leaves the spring at the equilibrium (x=0) point with 3.23m/s. Find the total distance (starting from rest) traveled by the mass. (Answer= 4.35)

yea i got my other homework questions but this one confused me. The solution is probably simple, but i have the tendency to overthink. Thank you for the help.

Homework Equations

PEs -umg(0.8) = KE

The Attempt at a Solution

1/2(200*x2) - (0.15*10*9.8*x)= 1/2 (10*v2)

then i used the quadratic formula to find x, but i got like 0.76 i think.

 

[Fightfish]

There is no need to consider the elastic potential energy; the question already tells you that the mass leaves the spring with a certain velocity, hence you can safely ignore the spring from then on.

 

[ismailmustafa]

Yeah, start with when the mass leaves the spring. There is no need to take the spring into consideration. It is just there to confuse you. When it comes to these problems, it's best not to over think them other wise you can get overwhelmed easily if you're just starting out. Spend time reading the problem rather than solving. Good Luck.