HELP! mcat physics - two masses one force

[nontradstudent16]

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I understand that mass will not affect the time that two objects are dropped onto the ground. In this case the fact that it is a spring doesn't seem to matter...The explanation in the back of the book (EK 9th edition) only says that it should be obvious that mass doesn't affect height. I am wondering if since the force on both of the objects is the same, then wouldn't the mass differences necessarily cause a difference in acceleration (ala f=ma)? Thanks!

 

[deleted853480]

.5kx^2= m1gh1 +m2gh2

 

[deleted853480]

Each object should receive half the amount of the energy stored in the spring. So the answer is B

 

[BobbyKoch]

I believe the answer is C.

The force is the same on both objects because, as far as the spring is concerned, they are one object of mass 3m.

1/2kx^2=3mgh

 

[PlsLetMeIn21]

The objects are moving together, so they have the same velocity and it was generated over the same time, so they have the same acceleration. But because they have different masses, they are not experiencing the same force. Mass A experiences 2/3 of the total force and Mass B experiences 1/3 of the total force.

But why look at force? Energy is what matters. For Object A, 0.5 Ma va^2 = Mgh, where Ma cancels, leaving 0.5va^2 = gh. The same is true for Object B, so we have va^2 = 2gh AND vb^2 = 2gh. They move together, so va = vb, resulting in the same height reached for both objects, choice C.

 

[BobbyKoch]

Best explanation. Thank you.

 

[nontradstudent16]

The objects are moving together, so they have the same velocity and it was generated over the same time, so they have the same acceleration. But because they have different masses, they are not experiencing the same force. Mass A experiences 2/3 of the total force and Mass B experiences 1/3 of the total force.

But why look at force? Energy is what matters. For Object A, 0.5 Ma va^2 = Mgh, where Ma cancels, leaving 0.5va^2 = gh. The same is true for Object B, so we have va^2 = 2gh AND vb^2 = 2gh. They move together, so va = vb, resulting in the same height reached for both objects, choice C.

Thank you!!