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Princeton Review AP Physics B Question

matt110029matt110029 Registered User Posts: 8 New Member
edited November 2012 in AP Tests Preparation
On page 94, there's a diagram with a cart on the top of a loop. At the bottom of the page it says:

Example 6.5: In the previous example, if the net force on the car at its topmost point is straight down, why doesn't the car fall straight down?
Solution: Remember that force tells an object how to accelerate. if the car had zero velocity at this point, then it would certainly fall straight down, but the car has a nonzero velocity (to the left) at this point. The fact that acceleration is downward means that, at the next moment v will point down to the left at a slight angle, ensuring that the car remains on a circular path, in contact with the track.

In the last statement, should't it be down to the right at a slight angle because acceleration is directed toward the center of the circle the entire time?

In case you don't have this book, the cart enters the loop from the left to the right.
Post edited by matt110029 on

Replies to: Princeton Review AP Physics B Question

  • WiseGuyWiseGuy Registered User Posts: 349 Member
    I don't have the book, but I see that in the solution, they say that the nonzero velocity is currently to the left (this is correct, as v is tangential to the circle at any moment in time, so it is directly left at the top of the circle). At the next moment, v will be slightly below where it was before (just below the -x axis) because at the top of the circle, the net force was downward (i.e. accel. was toward the center of the circle). Or, you can think of it that at the next moment in time, the car is just left of the top of the circle, going counterclockwise, so the acceleration is still toward the center and the v vector is perpendicular to the a vector.

    It does sound like what you described in the picture is also correct, but whether or not what's in the picture matches the solution, the solution is definitely correct. If you feel like scanning the picture or re-drawing it in Paint, or finding something similar online, I'd gladly explain it further.
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