Why is the Height of a Mass Launched by a Spring Dependent on its Mass?

[syang9]

this problem came up in my mcat physics prep book. two masses, one twice as massive as the other, are placed on a platform atop a spring. when they're launched, what height do they achieve?

i know they reach the same height, and from a previously archived thread on this board, i understand (somewhat) the reason.. the elastic potential energy is first transformed to kinetic energy, which is then transformed to gravitational potential energy. equating the formulas for those two energies results in an expression that is independent of mass.

what confuses me is that this seems to imply that the height of a mass launched by a spring is independent of mass altogether. this is clearly false.. could someone explain why?

 

[syang9]

also, why is it incorrect to simply equate the elastic potential energy to the gravitational potential energy? this yields an expression that is clearly dependent on mass.

 

[Doc Al]

the elastic potential energy is first transformed to kinetic energy, which is then transformed to gravitational potential energy. equating the formulas for those two energies results in an expression that is independent of mass.

For a given launch speed, the height reached is independent of mass (equate KE to GPE). But the launch speed depends on the mass (equate the spring PE to KE).

what confuses me is that this seems to imply that the height of a mass launched by a spring is independent of mass altogether. this is clearly false.. could someone explain why?

It doesn't imply that.

Can you state the exact problem?

also, why is it incorrect to simply equate the elastic potential energy to the gravitational potential energy? this yields an expression that is clearly dependent on mass.

It's not incorrect at all.

Perhaps you are mixing up (1) Two masses launched together, with (2) Each mass launched separately?

 

[tiny-tim]

hi syang9 !

also, why is it incorrect to simply equate the elastic potential energy to the gravitational potential energy? this yields an expression that is clearly dependent on mass.

I'll just add this to what Doc Al has said:

you can equate them, but how would that tell you how much of the energy goes to one mass, and how much to the other?

 

[syang9]

For a given launch speed, the height reached is independent of mass (equate KE to GPE). But the launch speed depends on the mass (equate the spring PE to KE).

so then, the reason that two masses launched together reach the same height is because the launch speed is determined by the total mass, right? after they are launched, they must reach the same height because they are traveling at the same speed.

 

[Doc Al]

Right!