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I'm sorry i couldn't write the problem out so i just scanned the photo instead. We did this problem in our phase test at school and i got it wrong and since i did and not given the papers back i would like to understand the problem with your help.
Photobucket link
HTML Code:http://i37.photobucket.com/albums/e65/TrippedCameron/Physics-1.jpg
Many thanks
Cameron
Ah, good old mechanics!
1.The linear velocity at the bottom of the loop
You know the acceleration from g, the incline of the loop, the mass, the distance it travels. Plug your values into the time-distance-velocity-acceleration formulas to arrive at the answer (and you can say how long it takes the rollercoaster to get there too)
2. Its angular velocity at the top of the loop
Again just a matter of looking up the formulas and plugging in the numbers. Look up angular velocity, angular acceleration or centripetal force in your mechanics textbook!
3. Braking force required to stop it
Isn't this given in the question?
If you had to work it out, I think you would calculate the rollercoaster's momentum when it reached the horizontal track, and the work done in bringing it to a stop, would equal this momentum. And work equals force applied X time. Maybe they made a mistake and want you to figure out how long it takes to come to a stop. In that case work out the decelleration on the rollercoaster due to the braking force (F=ma) and work out the initial velocity, and then use the time-distance-velocity-accelleration formulas with the distance it travels, to work out how long this takes.
I hope this is useful!
P.S. It is much easier to answer your question if you tell me what it is you got wrong - then I know what you didn't understand! (I hope I haven't told you anything wrong, it's been a while since I studied this!)