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Block sliding on curvilinear surface



Hello all:

I was thinking about writing an article for TPT on frictionless blocks sliding and leaving curvilinear surfaces using an algebraic approach. The most common example is a block sliding down a hemispherical surface, with and without friction. I was thinking instead about the following problem:

A block with mass m, originally at rest slides downward on a curvilinear surface given by y = (9x)^1/2 and r = 9cot(angle) cos(angle). This is a parabola on its side. Does the block leaves the surface before reaching the ground (y = 0)? What is the minimum value for n in such way that the block will leave the surface? (y = (nx)^1/2)

The first thing I noticed is that, in my opinion, you cannot use centripetal dynamics.

Two questions:
1. Is this an original problem? I highly doubt it (There is nothing new under the Sun) but I have never seen this type of problem before.
2. Is it solvable, even with simple calculus? Is it solvable algebraically?
3. Are there other simple curves where this type of problem could be solved?

Any suggestions will be appreciated.

Thanks,

Wilson J. Gonzalez-Espada, Ph.D.
Asst Professor of Physical Science/Science Education
School of Physical and Life Sciences
Arkansas Tech University
1701 N. Boulder Ave. (McEver Hall)
Russellville, AR 72801
(479) 968-0293
(479) 964-0837 fax

---------- Original Message ----------------------------------
From: Herbert H Gottlieb <herbgottlieb@JUNO.COM>
Reply-To: Forum for Physics Educators <PHYS-L@list1.ucc.nau.edu>
Date: Wed, 16 Jun 2004 07:56:05 -0700

The New York State Department of Education prepares yearly examinations
in
physics for its high school students. Back copies of past examinations,
together with answer keys, can be downloaded from the internet
by clicking on:

http://www.nysedregents.org/testing/scire/regentphys.html for exams given
in years 2001-2004

and clicking on
http://www.nysedregents.org/testing/scire/arcphys.html for exams given
in years 1997-2001.

Herbert Gottlieb
---
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