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Re: Spring Problem





On Wed, 29 Oct 1997 SSMOTHERMAN@MSCC.CC.TN.US wrote:

I have a question that, on the surface, appears so simple, I'm
embarrased to ask it. But it's something that has me stumped. Maybe there is
something obvious that I'm overlooking.
We have a horizontal, unstretched spring connected at one end by a
rigid support. I want to apply a force at the other end to stretch the spring.
By the 3rd law, the force I exert to the right (F=kx) will always be equal in
magnitude to the force that the spring exerts back to the left (F=-kx). In
this case, how can there ever be an acceleration of the end of the spring?

Steven Smotherman
Motlow State CC
Tullahoma, TN



This is a variation of one of my favorite essay exam questions, which goes
back to the horse-and-buggy days.

A horse is harnessed to pull a wagon. The horse exerts a force F in the
forward direction. Newton's third law tells us that the wagon must
therefore exert an equal and opposite force F--in the backward direction.
These two equal and opposite forces add to zero. Newton's law, F=ma tells
us that if the force is zero, the acceleration is zero. If the cart (and
horse) don't accelerate, they can't get moving from rest. So the horse can
never pull the cart anywhere. In fact, using the same logic, nothing in
the universe can ever move anything else by the application of a force.
Discuss.

Answer:

The "apparently logical" text of the problem is a fraud. The
"action-reaction" forces described by Newton's third law always act on
*different* bodies. The "net force" required in Newton's second law is the
total of all forces acting upon *one* body (or a system of bodies).

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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