Crystal Math XIV: cats

[⛄]

I think it's time for a new math quiz (this time involving physics):

Two cats are standing on a roof.
Which one falls off first?

[H.E. VOLODYMYR ZELENKSYY]

The one with the lowest µ.

[muon2]

What are the parameters of the cats and the roof? In particular does friction apply?

[⛄]

What are the parameters of the cats and the roof? In particular does friction apply?

Alfred already got it right.

[H.E. VOLODYMYR ZELENKSYY]

What are the parameters of the cats and the roof? In particular does friction apply?

Well, it's not in space.

[muon2]

What are the parameters of the cats and the roof? In particular does friction apply?

Alfred already got it right.

He can't have as it is worded. The problem says the cats are standing on the roof. The problem doesn't say the roof is sloped as it should, but I'm going to assume that a slope is implied (in areas that favor flat roofs there would be quite a bit of confusion). If they are standing at rest on the sloped roof then they are held in place by static friction. The value of mu for static friction determines the maximum force that the static friction can resist. Since both cats are standing at rest then both have a net gravitational force along the roof less than that of static friction and both will remain in place. In other words neither can fall off since both will remain still, barring some other external force.

For the cats to fall off they must start the problem in motion or must be instantaneously set on the roof. Then mu would refer to the coefficient of sliding friction which is the only value that is connected to the time it takes to fall. However, neither of those conditions are implied in the problem. Then one gets to the issue of parameters such as the distance to the edge of the roof which also would affect the answer.

Here's a question that would lead to the answer Alfred gave. Note how the extra words make all the difference.

Two cats are placed at the same time on a sloped roof with a rough surface at an equal distance from the edge of the roof. When they are placed on the roof they immediately begin to slide. What factor best determines which cat will fall off the edge first?
 

[⛄]

What are the parameters of the cats and the roof? In particular does friction apply?

Alfred already got it right.

He can't have as it is worded. The problem says the cats are standing on the roof. The problem doesn't say the roof is sloped as it should, but I'm going to assume that a slope is implied (in areas that favor flat roofs there would be quite a bit of confusion). If they are standing at rest on the sloped roof then they are held in place by static friction. The value of mu for static friction determines the maximum force that the static friction can resist. Since both cats are standing at rest then both have a net gravitational force along the roof less than that of static friction and both will remain in place. In other words neither can fall off since both will remain still, barring some other external force.

For the cats to fall off they must start the problem in motion or must be instantaneously set on the roof. Then mu would refer to the coefficient of sliding friction which is the only value that is connected to the time it takes to fall. However, neither of those conditions are implied in the problem. Then one gets to the issue of parameters such as the distance to the edge of the roof which also would affect the answer.

Here's a question that would lead to the answer Alfred gave. Note how the extra words make all the difference.

Two cats are placed at the same time on a sloped roof with a rough surface at an equal distance from the edge of the roof. When they are placed on the roof they immediately begin to slide. What factor best determines which cat will fall off the edge first?
 

LOL. You still don't get it, do you?

[politicallefty]

From what I've read of muon2, I'm pretty sure he knows his math and science.

[muon2]

From what I've read of muon2, I'm pretty sure he knows his math and science.

The implication is that I can't tell which questions in the series are jokes and which are serious. That's true, since I write serious questions in these fields for a living. So, if some of the questions in the series are serious and some aren't, I'm not likely to be able to tell which aren't until someone points out that a particular question isn't serious. I've seen plenty of attempts at serious questions from students that miss key concepts, so I'm trained to react to those.

[politicallefty]

The implication is that I can't tell which questions in the series are jokes and which are serious. That's true, since I write serious questions in these fields for a living. So, if some of the questions in the series are serious and some aren't, I'm not likely to be able to tell which aren't until someone points out that a particular question isn't serious. I've seen plenty of attempts at serious questions from students that miss key concepts, so I'm trained to react to those.

I hope you didn't take that wink as some sort of attack on your credentials. The wink was intended towards the OP. My point was that you actually do know your math and science.

[⛄]

From what I've read of muon2, I'm pretty sure he knows his math and science.

The implication is that I can't tell which questions in the series are jokes and which are serious. That's true, since I write serious questions in these fields for a living. So, if some of the questions in the series are serious and some aren't, I'm not likely to be able to tell which aren't until someone points out that a particular question isn't serious. I've seen plenty of attempts at serious questions from students that miss key concepts, so I'm trained to react to those.

It's the first and only joke question in this series.

If you wanna participate in a serious math debate, try my new thread π vs. τ.


P.S.: Wait... I've got another math joke question:

What does a mathematician do about constipation?
He works it out with a pencil.