Projectile Motion and Energy

[Medgen]

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I am working on an problem that I think might have the wrong answer. Could someone please confirm my rationale?

The problem states that objects A and B are placed on the same spring and that Object A has twice as much mass as object B. The question asks what would happen to objects B and A if the spring is depressed and released, propelling the objects into the air?

The answer indicates that they will rise to the same height.

I don't think that they would... If we use energy and say that since the same force over the same distance is applied to them, then they will have the same kinetic energy, then it follows that they will have different velocities because their masses are different. Therefore, they will have different heights. Does that make sense?

 

[GreenRabbit]

This would make sense if they were placed on separate springs. But because they are placed on the same spring, the spring will accelerate both of them at the same rate (as if they were one object), and so their exit velocities will be the same. Same exit velocities = same height achieved.

 

[justhanging]

This would make sense if they were placed on separate springs. But because they are placed on the same spring, the spring will accelerate both of them at the same rate (as if they were one object), and so their exit velocities will be the same. Same exit velocities = same height achieved.

I don't think that is what she meant. Same spring as in same spring constant but different times. Otherwise their be not point to this question.

 

[GreenRabbit]

I don't think that is what she meant. Same spring as in same spring constant but different times. Otherwise their be not point to this question.

Just looked it up, this is from EK1001 q328. It says "A 2kg ball and an 8kg ball are placed on the same spring at the same time..."

But perhaps you're right, she might not have seen that phrase. It's hard to miss though because the other questions around it ask the same thing but tell you to use separate springs (and have the same answer choices), so the distinction sticks out.

 

[Medgen]

So then their kinetic energies are not equal when they first begin their projectile motion? If they have the same force applied to them over the same distance then they should have the same kinetic energy... but if they had the same kinetic energy then how would 1/2 mv2=1/2 mv2? Since the masses are different, it would seem that according to this, if we had equivalent kinetic energies then we would have different velocities.

 

[GreenRabbit]

So then their kinetic energies are not equal when they first begin their projectile motion? If they have the same force applied to them over the same distance then they should have the same kinetic energy... but if they had the same kinetic energy then how would 1/2 mv2=1/2 mv2? Since the masses are different, it would seem that according to this, if we had equivalent kinetic energies then we would have different velocities.

They have different energies leaving the spring.

 

[Medgen]

But they shouldn't... the spring exerts the same force on them at every point in the motion and therefore does the same work on them. Sorry for the confusion. I really appreciate the help!<br>

 

[GreenRabbit]

As long as they are on the same spring at the same time, the spring will exert different forces on each of them. Think about it, how could it accelerate one object faster than the other? The spring must be in constant contact with both of them as the energy is being released.

 

[Medgen]

That makes sense! Thanks!<br><br>

 

[banner18]

So then their kinetic energies are not equal when they first begin their projectile motion? If they have the same force applied to them over the same distance then they should have the same kinetic energy... but if they had the same kinetic energy then how would 1/2 mv2=1/2 mv2? Since the masses are different, it would seem that according to this, if we had equivalent kinetic energies then we would have different velocities.

The KE's are equal, that is the only way both objects can reach the same height. I think youre not sure why this is case since they have different velocities. The smaller object will experience a higher velocity because it will have a higher magnitude of acceleration a=F/m (small mass over same force=higher acceleration). But both will have the same KE since the higher mass of one object will offset the high velocity of the other object.


never mind im stupid my explanation makes zero sense.. the lighter ball should go higher. now i dont get it...

 

[Medgen]

The KE's are equal, that is the only way both objects can reach the same height. I think youre not sure why this is case since they have different velocities. The smaller object will experience a higher velocity because it will have a higher magnitude of acceleration a=F/m (small mass over same force=higher acceleration). But both will have the same KE since the higher mass of one object will offset the high velocity of the other object.


never mind im stupid my explanation makes zero sense.. the lighter ball should go higher. now i dont get it...

They do not have the same KE and they do not have the same potential energy... the reason for this is because they have different masses. They do, however, reach the same height because they have the same initial velocity. They have the same initial velocity because they are both released at the same point and accelerate throughout the spring's motion at the same rate.