Why Do Equal Forces on Different Masses Result in the Same Height?

[mrlucky0]

Homework Statement

Object A and B are placed on a spring. Object A has twice as much mass as object B. If the spring is depressed and released, propelling the objects into air, object A will:

answer: rise to the same height as object B

Homework Equations

The Attempt at a Solution

Based on my reasoning and math, I am confused why both objects would rise to the same height:

The force on both objects is the same, F. And 2*mass of B = mass of A

F = (mass of A)*(accl. A) = (mass of B)*(accl. B)
F = 2*(mass of B)*(accl. A) = (mass of B)*(accl. B)

cancel out (mass of B):
F = 2*(accl. A) = (accl. B)

Since the upward acceleration of B is twice the that of A, why would the height be the same?

 

[tyco05]

I've only briefly thought about your attempt:

You are only considering the upward forces due to the spring.

What about the force on each object due to gravity... will it be the same?

Consider...

 

[HallsofIvy]

I think the simplest way to do this problem is to use "conservation of energy". The spring has a specific amount of energy stored in it when compressed and, on release gives the same energy to A and B. They will rise to heights that give the same potential energy to both.

 

[get_physical]

any one know how to approach this problem?

 

[Dadface]

As the spring moves up A and B are pushed up with at all times equal speeds and their speeds are also equal when they lose contact with the spring.Take it from there.