Mail Time: 5 Steps 2005 vs. 2010 edition

Linda Hoover writes in with a pertinent question:

My oldest son, Daniel used your "5 Steps to a 5 AP Physics B&C" 2005 lime green edition to study for the AP Physics B exam in 2007. He really enjoyed using your book and he in fact, scored a 5! Thank you!

Glad it worked.  Awesome.

My youngest son, Mike is currently taking AP Physics with the plan to take the AP Physics B exam this May. We still have our 2005 version of your bookthat we could use for the review but I noticed that you have 2 later versions, 2008-9 and 2010-11.

Question 1: Have the typos/errors in the [previous versions] been fixed in the latest 2010-11 version?

Yes, as far as I can tell. I don't know whether most of these were my fault or the typesetter's, but the current edition's editor was extremely thorough and (most importantly) knowledgable about physics. I've found one small mistake already that I mentioned and fixed on this blog, but I don't think anything major. (And, I think folks online have exaggerated the frequency of errors. But, whatever, errors are annoying, to readers and to me.)

Question 2: How different is the 2010-11 version from the earlier 2005 copyright?  Should we just use the book we already have (2005) or buy the updated 2010-11 version?

Well, I've made a good deal of editorial changes to the text to make it more readable; plus, we've reordered things to emphasize what's truly important. After the first edition sold well, McGraw-Hill listened more attentively to me about some issues. The figures have been redrawn professionally, the layout is much clearer...

That said, much of the content is similar, and the exams themselves haven't changed. The 2005 book won't hurt, and will save you the 20 beans. If you buy a new one, however, I think I get 25 cents in royalties! :-)

Good luck... let me know if you have comments about the 2010-11 edition.

GCJ

Three masses connected over a pulley

In my 5 Steps to a 5 AP Physics prep book, page 70 is a review of tension problems, also known as many-body problems.  I give eight different situations in which blocks are connected by ropes.  The goal of each problem is to find the tension(s) in the rope(s), and the acceleration of the system.

The approach that I advocate is to draw a separate free body diagram for each block, then write Newton's second law separately for each block.  The acceleration and tension(s) are solved for by adding the Newton's second law equations together.

Ruth Mickle, of Atlanta, noted yesterday that she gets a different answer to problem 6 than is printed in the book.  I agree -- for whatever reason, the answer in my book is wrong.  Below I give a thorough solution. 

The problem shows three blocks connected by strings over a pulley, as shown at the top of the post.  Given that m is 1.0 kg, the question asks for the tensions and acceleration.

Start by drawing three free body diagrams.  Note that the two ropes will have two tensions; I'll label these T1 and T2.

The acceleration will be toward the heavier blocks.  Thus, the mass m will accelerate upward, and the other masses will accelerate downward.  So when we write Newton's second law, for mass m we'll write "up forces - down forces = ma."  For the other masses, we'll write "down forces - up forces = ma."  Always start Newton's second law in the direction of the acceleration.

T2 - mg = ma          2mg + T1 - T2 = 2ma                       4mg - T1 = 4ma

Now, add 'em up.  Note that the T1s and the T2s will cancel in the addition:

-mg + 2mg + 4mg = 7ma

Solving for a, we get a = (5/7)g, or 7.1 m/s².

Now just plug back into the equations above to find that T2 = 17 N, and T1 = 11 N.