Aamc 11 #44

[Bancrofti]

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Don't really understand the answer fully.

Question is:
Which of the following constraints applies to the suspension angle theta (in radians) of the car shown in Figure 1?

I understand why it has to be equal to or greater than 0, since the angle was said to be proportional to the rotation velocity. However, I don't get where from the passage we were supposed to extrapolate that the maximum angle is 90 degrees. Further, I guess I'm not good with radians, but how does pi/2 = 90? going to look that part up once I'm done reviewing this section.

 

[paul411]

pi/2 = 90?

Thats just by definition. 2pi radians is 360° (circle). You just need to remember that.

 

[MT Headed]

The scenario is analogous to swinging a yoyo around your head. If you grab a yoyo by the string and hold it above your head, it hangs at 0 degrees. If you start swinging it in a circle, the string angle (from vertical) could be 45 degrees. If you swing it really hard, you could get it all the way to horizontal 90 degrees. Could you ever swing it so hard that it got up to 150 degrees? no.

This question tested both a concept and a conversion. I almost answered it by thinking "well, 90 degrees is a quarter of a circle, so it's pi/4". 😱 Then I fixed it. The MCAT asks the simplest questions in the most complicated ways.

 

[harryking]

If you think about it, there is really no force acting on the car vertically besides gravity therefore it will never reach 90 degrees although it could get really close.

 

[Bancrofti]

Thanks you guys. Sometimes I fail to think conceptually and want everything to fit in to a "this question uses this formula" type question. I simply wasn't familiar with the radians aspect of things, which I now know thanks to you guys. However, I wasn't analyzing the situation properly to come up with the fact that the car couldn't go past 90 degrees.

I love the yoyo example btw. You should teach if you thought of that by yourself.

 

[cycloethane]

A more mathematical explanation is can be found in Berkeley Review: force pointing down in a car is mg. The force pointing up is (mv^2/r)*costheta. So, as theta approaches 90 degrees, it gets more and more difficult to make it go up. It can never actually be 90 degrees since then there would be only gravity pointing down.