Kinetics of discs vs wooden block vs hoop/loop please help!

[clc8503]

I took the MCAT last year and the very first passage was about the Kinetic Energy, Momentum, Velocity or something along those lines regarding a hoop/loop, a disc, and a block of wood on an incline. Very little numerical info was given in the passage, which was then followed by questions regarding the kinetics of these various objects, based on their shapes (Ex: hoop/loop, wooden block, and a disc) Questions also arose that asked which object would descend down the incline with the greatest velocity. Of course I knew K.E.= mv/2 and that p=mv, but apparently that wasn't enough to answer the questions. I just remember staring at the computer screen for 5 minutes, thinking wtf? I have read through my KAPLAN book, my Princeton Review Book, and my Exam Kracker Book, and nowhere have I found anywhere in these books anything that's describes an objects kinetics, based on that objects shape. I'm taking the MCAT again in March, and I am still clueless as to how I am to approach such a problem. Was this concerning Conservation of Energy? Was this possibly an Inertia problem? Can someone please point me in the right direction? A reference source? A website explaining this? Anything? PLEASE!!!!!!!! I'm desperate to understand this.

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[EdCLS]

I am very possibly completely wrong here, because it's been a long time since I've had physics and I haven't gotten to these concepts in my MCAT review yet. Please take what I'm saying with that in mind, and realize that someone more insightful and well-versed in physics will probably be along shortly to answer, as well.

I would approach this from an energy and inertia standpoint, and you can answer it qualitatively (again, if my understanding is correct, which it may not be). I'm also assuming this to be a frictionless incline. I'll also assume that the hoop and disc are rolling without slipping down the incline and that the hoop and disc each have the same mass.

There are two forms of energy to consider here: rotational kinetic energy and translational kinetic energy. If they're being released from the same incline, the only energy available to pull them down the incline is gravitational potential energy.

Conservation of energy tells us that the gravitational potential energy will be converted into kinetic energy to move the objects down the incline.

For the block, all we have is translational kinetic energy and no rotational kinetic energy to consider. For this case, PE=KE. For the MCAT's purposes, all of the gravitational potential energy is converted to kinetic energy for the block.

The hoop and the disc will each have rotational kinetic energy (rKE) in addition to translational kinetic energy (tPE). In this case, PE=KE + rKE. As such, not all of the gravitational potential energy (GPE) in these cases is converted to translational kinetic energy (the kind that generates the velocity). Given that, we know the block will descend the incline the fastest because all of the GPE is converted into tKE.

Now the question is: of the hoop and the disc, which one will acquire the greatest downward velocity? Consider the equation for rotational kinetic energy: rKE=(IW^2)/2. The difference in inertia between the two will dictate the difference in rotational kinetic energy between the two. Recall that objects with more of their mass near their rotational axis have lower inertia, and objects with more of their mass away from their rotational axis have more inertia (resistance to change in rotation).

From that standpoint, the ring/hoop will have more inertia, and will therefore have more rotational kinetic energy. In other words, more of the GPE will be converted to rPE for the hoop because it takes more energy to get the hoop moving. The disc will have less rPE and will therefore end up with more tPE, which means the hoop will go faster.

In the end, I'd say the final velocities of these three objects would be block > disc > hoop. Again, to stress: this is because the block has no rKE, so all of the initial GPE is converted to tKE. The more rKE an object has, the less energy is converted to tPE.

Again, I could be entirely incorrect here, because it's been a long time since I've had this. But that's what I would say if faced with that passage. In any case, I hope this is helpful.

Good luck!

 

[clc8503]

I am very possibly completely wrong here, because it's been a long time since I've had physics and I haven't gotten to these concepts in my MCAT review yet. Please take what I'm saying with that in mind, and realize that someone more insightful and well-versed in physics will probably be along shortly to answer, as well.

I would approach this from an energy and inertia standpoint, and you can answer it qualitatively (again, if my understanding is correct, which it may not be). I'm also assuming this to be a frictionless incline. I'll also assume that the hoop and disc are rolling without slipping down the incline and that the hoop and disc each have the same mass.

There are two forms of energy to consider here: rotational kinetic energy and translational kinetic energy. If they're being released from the same incline, the only energy available to pull them down the incline is gravitational potential energy.

Conservation of energy tells us that the gravitational potential energy will be converted into kinetic energy to move the objects down the incline.

For the block, all we have is translational kinetic energy and no rotational kinetic energy to consider. For this case, PE=KE. For the MCAT's purposes, all of the gravitational potential energy is converted to kinetic energy for the block.

The hoop and the disc will each have rotational kinetic energy (rKE) in addition to translational kinetic energy (tPE). In this case, PE=KE + rKE. As such, not all of the gravitational potential energy (GPE) in these cases is converted to translational kinetic energy (the kind that generates the velocity). Given that, we know the block will descend the incline the fastest because all of the GPE is converted into tKE.

Now the question is: of the hoop and the disc, which one will acquire the greatest downward velocity? Consider the equation for rotational kinetic energy: rKE=(IW^2)/2. The difference in inertia between the two will dictate the difference in rotational kinetic energy between the two. Recall that objects with more of their mass near their rotational axis have lower inertia, and objects with more of their mass away from their rotational axis have more inertia (resistance to change in rotation).

From that standpoint, the ring/hoop will have more inertia, and will therefore have more rotational kinetic energy. In other words, more of the GPE will be converted to rPE for the hoop because it takes more energy to get the hoop moving. The disc will have less rPE and will therefore end up with more tPE, which means the hoop will go faster.

In the end, I'd say the final velocities of these three objects would be block > disc > hoop. Again, to stress: this is because the block has no rKE, so all of the initial GPE is converted to tKE. The more rKE an object has, the less energy is converted to tPE.

Again, I could be entirely incorrect here, because it's been a long time since I've had this. But that's what I would say if faced with that passage. In any case, I hope this is helpful.

Good luck!

Thanks for that fully descriptive explanation! What you said really did make a lot of since. If you knew this with minimal MCAT studying, and it being years since you had Physics, I think its safe to say that you're going to murder the PS section of the MCAT Good luck with the rest of your studying. When do you plan on taking the MCAT?

Anyone else care to critique this? Any comments are greatly appreciated

 

[EdCLS]

I should've said that they were ignoring friction earlier, rather than saying "frictionless." If the incline was frictionless, the hoop/disc would slide down rather than roll down. Still, I am pretty sure the above is what they were getting at.

Hopefully someone else can support or refute this for us.

Good luck!

 

[clc8503]

I should've said that they were ignoring friction earlier, rather than saying "frictionless." If the incline was frictionless, the hoop/disc would slide down rather than roll down. Still, I am pretty sure the above is what they were getting at.

Hopefully someone else can support or refute this for us.

Good luck!

EdCLS,

Does the "CLS" in your user name stand for Clinical Laboratory Scientist? If so, that's what by B.S. was in as well. It's tough to that full time and still make time to study for this thing

 

[unique135]

Here's the explanation http://hyperphysics.phy-astr.gsu.edu/hbase/hoocyl.html#hc1

Yea true, they were ignoring friction and it wasn't frictionless. Otherwise, there was no rotational energy.

clc8503, how well was the paragraph explained generally and also, in term of shapes and its relation to rotational inertia.

Nice catch, EdCLS.

 

[lixxx669]

I took the exact same test as yours and I totally got that question wrong too.....

Here the explanation http://hyperphysics.phy-astr.gsu.edu/hbase/hoocyl.html#hc1

Yea true, they were ignoring friction and it wasn't frictionless. Otherwise, there was no rotational energy. All I assume masses were equal.

clc8503, how well was the paragraph explained generally and also, in term of shapes and its relation to rotational inertia.

Nice catch, EdCLS.

The passage has NOTHING to do with rotational energy, not even a single word of "rotation", that's why this question is horrible.

 

[unique135]

I took the exact same test as yours and I totally got that question wrong too.....



The passage has NOTHING to do with rotational energy, not even a single word of "rotation", that's why this question is horrible.

What is your understanding for the passage (although there is no real passage)?

 

[clc8503]

I took the exact same test as yours and I totally got that question wrong too.....



The passage has NOTHING to do with rotational energy, not even a single word of "rotation", that's why this question is horrible.

If it had nothing to do with rotational energy, which other than properties associated with inertia and frition, I didn't even think we had to know on the MCAT, what was it concerning? Im not looking for MCAT answers. I just want to be pointed in the right direction. What topic do I need to study to understand this? Did it even have anything to do with Center of Mass?

 

[EdCLS]

Clc8503:

I think what lixxx669 meant was that the passage did nothing to suggest that rotational kinetic energy should've been a consideration, which is why the question was perceived to be a poor one.