TBR Physics Ch 3 Passage 2 question 13

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Oct 25, 2010
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I'm trying to reconcile the answers between two different problems. Both are from the same passage and involve a roller coaster going through a loop.

Question 9 asked about the speed at the top of the loop if it could barely complete the loop. In its explanation, it states the acting forces are Normal force (down which is toward the center), Gravity (down), and Centripetal force (up).

Later in that passage in question 13, it asks to identify the force vector from pictures when the cart is half way up the loop. The answer states "the only forces acting on [the cart] are Normal force [left, toward the center] and gravity [down]." Why doesn't centripetal force (right, outside the circle) come into play here?

Why was I wrong in thinking that centripetal force would play into this? Or was the explanation worded poorly and Normal force is just so much larger than centripetal force that it gets cancelled out?

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Circular motion questions like these are particularly tough, especially if the explanation is poorly worded. I don't have the TBR books in front of me, but I can offer some general advice about thinking through the problem:

First, you've got to remember that "centripetal force" is a name we give to mean "whatever force is making something move in a circle". Remember that all things WANT to move in a straight line, so when they move in a circle there must be something accelerating them (changing direction) to keep them in a circle.

So when you're thinking through circular motion, one of the first questions to ask yourself is, "Okay but WHAT is providing the centripetal force?"

Nine times out of ten on MCAT problems, the answer is going to be tension in a string, the normal force, or gravity. It could be anything, but those are the three really popular ones among question-writers.

So in the case of a roller coaster car going around a loop, the thing pushing the car into circular motion is the normal force acting between the wheels of the car and the track. So you can always set Fc = Fn

Gravity, of course, is just always pointing down, and has nothing to do with the centripetal force. If gravity were the only thing in the picture, the car would just fall via the projectile motion equations.

I'm not looking at the particular questions you're referring to, but it sounds like the explanation is somewhat confusingly written if it has the Fn and Fc written as if they were different vectors. Here, the Fc *is* the Fn.

Based on what you've written, it sounds like the explanation to Q13 is the more technically correct one. At every point in the loop, the only forces acting on the car would be gravity and normal (and, I suppose friction and air resistance but we usually just ignore those).

Hope this helps!


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