Spring system: Relationship b/t mass and distance object travels

[sweetpete28]

A spring is at the bottom of a frictionless incline. When a box of mass M compresses the spring distance x and is released from rest, the box slides distance d up the incline (measured from where the box is at rest).

a) Suppose a box of mass 2M is used to compress the spring distance x,and is released from rest. The distance the box will slide up the incline is?

b)Suppose a box of mass M is used to compress the spring distance 2x, and is released from rest. The distance the box will slide up the incline now is?

For a) I am pretty sure that if the mass is doubled, the distance traveled will decrease, as I believe the acceleration would be cut in half. But how do I determine by exactly how much? What is relationship b/t mass and distance?

For b) the force is doubled so I think acceleration doubles but what about distance traveled?

Any advice? Please help...

 

[PeterO]

A spring is at the bottom of a frictionless incline. When a box of mass M compresses the spring distance x and is released from rest, the box slides distance d up the incline (measured from where the box is at rest).

a) Suppose a box of mass 2M is used to compress the spring distance x,and is released from rest. The distance the box will slide up the incline is?

b)Suppose a box of mass M is used to compress the spring distance 2x, and is released from rest. The distance the box will slide up the incline now is?

For a) I am pretty sure that if the mass is doubled, the distance traveled will decrease, as I believe the acceleration would be cut in half. But how do I determine by exactly how much? What is relationship b/t mass and distance?

For b) the force is doubled so I think acceleration doubles but what about distance traveled?

Any advice? Please help...

You are concentrating on acceleration - which can lead to the answer - but you have chosen not to consider Energy - which can give a global view of what is happening without going into each specific.