Your equation for N1 applied to m2 , "(mu)m1g - F(pull) = m2a2", is wrong.
You specified that the external force F(pull) is applied directly to m1
only. The only horizontal forces on m2 are frictional, and since its lower
surface is frictionless, the above equation should read:
(1) (mu)m1g=m2a.
Applying N1 to the entire 2-body system gives:
(2) F(pull) = (m1 +m2)a
Note that my equation (1) is valid whether or not there is slippage between
the two masses, with a = the acceleration of m2.
My equation (2) is also true in the event of slippage, but then a = the
acceleration of the CM of the two body system.
Note carefully that with slippage there are 3 pertinent (and numerically
different) accelerations: a1, a2 and a_(CM).
Bob Sciamanda
Physics, Edinboro Univ of PA (Em) http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "Gene Gordon" <physics@ROCHESTER.RR.COM>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Thursday, October 20, 2005 10:07 PM
Subject: Free body diagram misconception
| Hello all, I have a strange physics question that the 5 physics
| teachers at our high school sat and pondered today. We have started
| teaching AP-C physics and the teacher for this new course came to us
| with a variation to a question from the book. Here it is.
|
| Block 1 is at rest atop Block 2. Block 2 rests atop a frictionless
| surface. A force is applied to Block 1 pulling it to the right. The
| coefficient of friction between blocks 1&2 is some non-zero value less
| than 1. What is the Net force equation for Block 2?
|
| We drew the free body diagrams for both blocks and came up with the
| following equation for Block 2.
|
| (mu)m1g - F(pull) = m2a2
|
| Now all of us agreed on this, but we also saw a problem. This means
| that there is some value for the force of the pull that Block 2 will not
| move. However it is on a frictionless surface and IF they were
| connected the Frictional component would disappear - thus the object
| would accelerate. What is wrong with our reasoning? Did we make a bad
| assumption somewhere?
|
| I love these problems but it is driving me bonkers since I know that I
| am forgetting something fundamental --- Block 2 should accelerate for
| ANY force pulling on it if it is on a frictionless surface.
|
| Thanks in advance for any help.
|
|
| Gene Gordon
|