A roller coaster car on the frictionless track shown, starts from rest at height(adsbygoogle = window.adsbygoogle || []).push({}); h. The track is straight until point A. Between points A and D, the track consists of circle-shaped segments of radius R.

Question:

What is the maximum heighthmaxfrom which the car can start so as not to fly off the track when going over the hill at point C? Give you answer in terms of the radius R.

Hint:This is a two-part problem. First findvmaxat C.

My answer:

I have tried many different methods, but cannot find the right one. The answer in the textbook tells me that.hmax= 3/2R

I know how to findhmaxonce I havevmax, but the problem is findingvmaxin the first place.

I don't know what I'm supposed to do with the 30 degree angle. I thought of using it as the angular position, but I can't seem to continue from there to findvmax. I calculated that the angular position would be 60 degrees (90 - 30).

Does the fact that there are 2 circles have something to do with my answer? Or is that just there to confuse me?

I also tried drawing a FBD at point C. The only two forces I obtained were a normal force (up) and gravity (down). However, because it is a circle, is my normal force supposed to be pointing down also (toward the centre of the circle)? Does this have something to do with my answer also?

Please help-- I have tried many different methods but cannot seem to get the right answer.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Energy and Circular Motion

**Physics Forums | Science Articles, Homework Help, Discussion**