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Question for week of 10/26 - Oct 26, 2009 at 2:16PM
Dave Avatar
Dave
San Marcos, Texas
352 Posts

Things got a little hectic last week, so I'm a little late with a new question.  Here it is:

A particle is constrained to move in a circle with a 10-meter radius.  At one instant, the particle's speed is 10 meters per second, and is increasing at 10 meters per second squared.  The angle between the particle's velocity and acceleration vectors is

A. 0 degrees

B. 30 degrees

C. 45 degrees

D. 60 degrees

E. 90 degrees

Have fun!

Dave


Try not to become a man of success, but rather try to become a man of value -- Albert Einstein

Replies to Question for week of 10/26

Re: Question for week of 10/26 - Nov 03 2009 10:03AM
Gary
Society of Physics...
293 Posts

Hmm...I started to do V dot A = v*a*cos(theta) and solve for theta, but then it seemed like the numbers were picked so that it might be easier just to think it through in terms of components, so here goes...

...the particle's velocity is tangent to the circle, while the particle's acceleration, well, there's two pieces:
the toward-the-center-of-the-circle piece (v^2/R), and
the speeding-up-as-you-go-around piece (given)...

Oh! and since these two components come out to be the same size, then the answer is straight-forward...

From what I've been told and what little I can recall, many of the GRE questions are like this, where some symmetry, or unit analysis, can be used to get the answer with little or no computation. Anybody got another example where the symmetry or the units gets the answer quicker than a brute force computation?


NSF Program Director (on assignment from the AIP and the Society of Physics Students to serve as the Robert Noyce Scholarship Program Director at the National Science Foundation)