mass of projectile and conservation of mechanical energy

[IntelInside]

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Question from EK physics 1001:

"A 2 kg ball and 8 kg ball are placed on separate springs, each with the same spring constant. The springs are compressed by the same distance and released. Which of the following are true about the maximum heights reached by the ball.?"

Answer: A. the 2kg ball will go four times further.

I understand this answer and I did get it right but then we have this question

"A 2 kg ball and 8 kg ball are placed on the same spring at the same time. The spring is compressed and released. Which of the following are true about the maximum heights reached by the balls.?"

Answer: C. the balls reach equal maximum heights.

Is this because the potential energy of the spring is being converted to the potential energies of both balls? So it would be something like this:

PEspring = PEg8kgball + PEg2kgball
.5 k x^2 = 8x10xh + 2x10xh?


Can someone explain this in relation to the previous question? thanks

 

[loveoforganic]

Try to think about it intuitively. If you put two balls on a spring that is unable to flex in any direction but up and down, then when it's released from compression, it's going to reach a maximum velocity at its center point. Both the balls are on the same platform and thus reach the same maximum velocity.

 

[IntelInside]

ight so the way im thinking about it now is this.

for the first question:

the differences in forces Fnet = K*dx - mg = ma shows that the two objects will accelerate at different rates thus different velocities and the height will then be different

for the second question:

Both objects are experiencing the same Fnet so the acceleration is the same thus the velocities are the same. Since velocities are the same and mass is irrelevant in system with no atmospheric pressure they reach the same height.

 

[WashMe]

however fast the platform is moving at the last point of contact will be the initial velocity for any number of objects placed on the same platform. I mean, if the platform has a velocity of, say, 10 m/s, then whatever it flings will have an initial velocity no greater or less than 10 m/s.