Car behaviour on a straight road with a rolling road

[DrSelvigsApprentice]

Homework Statement

An extra-curricular theoretical assignment I have received:

A car is traveling on a completely flat/uniform straight road at a constant velocity on a clear, dry day. 100 meters ahead, underneath the road there is a roller (similar to a rolling-road) which can spin without restriction (and assume without friction). The roller is the same width as the road and is laid perpendicular to the direction of travel so both front wheels will make contact with it at exactly the same time. Only 0.05m of the roller is exposed to the road - the rest is underground. The question is how will the car behave when it drives over the roller and which physical forces need to be considered when determining the behaviour.

Homework Equations

NA

The Attempt at a Solution

My thinking is the car should carry on and the roller will spin. The car may lose a little velocity but I'd be embarassed to submit this as an answer without backing it up. Which physical forces/equations do I need to consider to deliver an answer. Can anyone provide some guidance please?

Thanks!

 

[phinds]

As the car moves down the road, what is the forward/backward velocity of the outer edge of the wheel at the point where it hits the road directly below the axle?

 

[DrSelvigsApprentice]

As the car moves down the road, what is the forward/backward velocity of the outer edge of the wheel at the point where it hits the road directly below the axle?

Hello Phinds - thanks for the response, trust you're well. I don't have any information about forward/backward velocity as requested. For the sake of modelling, and if easier, can we say the car is traveling at 30km/h?

 

[Nugatory]

My thinking is the car should carry on and the roller will spin.

Whether the roller spins or not depends on which of three different cases you're considering:
1) The car is in gear with the engine running to keep it moving against air resistance, friction, the rolling resistance of the tires, and everything else that causes a car to coast to a stop when the engine is running.
2) The car is not in gear with the engine running, so is gradually coasting to a stop because of air resistance, friction, the rolling resistance of the tires, and the like.
3) For purposes of this problem we are ignoring all these factors, so the car is coasting along without slowing down even though it is not in gear with the engine running.

That's three cases, but either the roller turns or it doesn't, so the answer will have to be the same for two of them.

 

[phinds]

Hello Phinds - thanks for the response, trust you're well. I don't have any information about forward/backward velocity as requested. For the sake of modelling, and if easier, can we say the car is traveling at 30km/h?

I wasn't asking if you had any such information, I was asking you to think about it.

 

[Nugatory]

I don't have any information about forward/backward velocity as requested

Yes you do, although you may not realize it. Think about the question for a moment - that's why he asked it.

 

[DrSelvigsApprentice]

That's three cases, but either the roller turns or it doesn't, so the answer will have to be the same for two of them.

Thanks. Without posting lots of back and forth on the forum about this as I have a lot to learn, what would you recommend I delve into to further my knowledge and come out with a strong answer?

 

[Nugatory]

Thanks. Without posting lots of back and forth on the forum about this as I have a lot to learn, what would you recommend I delve into to further my knowledge and come out with a strong answer?

You need to understand Newton's three laws and $F=ma$ (which is just the second law in modern form) but that's about it. This problem doesn't involve any arcane physics, it's just a bit harder to visualize how to apply Newton's laws here than if we were sliding a block around on a frictionless surface.

 

[phinds]

I would suggest that before you worry about formulae and such, THINK about my question and get the answer.

If you can't understand a physical situation it won't do you any good to have formulae since you won't know which to apply.