# Homework Help: Two objects launched into the air by identical springs

1. Oct 22, 2009

### fattydq

Two objects with DIFFERENT MASSES are launched vertically into the air by identical springs. The two springs are compressed by the same distance before launching. Which of the following statements is or are true? (NOTE: THERE MAY BE MORE THAN ONE TRUE STATEMENT).
A) Both masses reach the same maximum height
B) Both masses leave the springs with the same energy
C) Both masses leave the springs with the same speed
D) Both masses leave the springs with the same Kinetic Energy
E) The lighter mass will gain more gravitational potential energy than the heavier mass.

this actually isn't a homework question, but it's posed at the beginning of a chapter in my book and I'm trying to work through it and figure it out before I read the chapter, kind of to challenge myself, since I have no other homework tonight : )

I know I can rule D out immediately, since the formula for kinetic energy directly involves multiplying by mass, and thus I can rule B out right? I also think I can rule A out, just due to common sense (if a spring were launching an elephant and a ping pong ball, the elephant might barely move while the ping pong ball would fly into the air)

For E I thought it was the opposite? Wouldn't the heavier mass gain more potential energy?

So I think I'm left with C....I could be terribly wrong though and I'd love to discuss this with you guys!

2. Oct 22, 2009

### ill

since the equation for the energy of a spring is .5kx^2 and doesnt involve mass, one could say the masses leave the springs with the same energy. and for part E the potential energies would be the same since kx^2 is directly proportional to mgh---increasing mass would only decrease height proportionally and vice versa

3. Oct 22, 2009

### fattydq

Ahh that makes sense, thanks, I forgot to consider that equation for the energy of a spring.

So B and C are viable, yes? Any other notes of interest in this problem?

4. Nov 14, 2009

### dl1245

Not so fast on ruling out D..
Yes, KE= .5mv^2, and the masses are different,but the speeds at which they are launched at are also different, which could give you the same KE product..