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Re: [Phys-l] real-world mechanics problem



To clarify why this is a good transfer problem, although I'm repeating much of what JD said: You can't solve the problem by plugging numbers into an equation. You can't solve the problem using a memorized procedure from a homework or in-class problem. Yet, if you understand the underlying physics principles, you can solve the problem. A good transfer problem generally evokes responses, verbal or unspoken, from students such as, "But we've never done a problem like this before! We've never dealt with more than one pulley system. This isn't fair!" I recall in my HS physics class (worst class and worst teacher ever) that we solved pulley problems by counting the number of ropes between pulleys and plugging into a formula. Absolutely no understanding involved.

Bill



On Jan 31, 2011, at 3:38 PM, John Denker wrote:

On 01/29/2011 10:45 PM, Stefan Jeglinski wrote:

So, I'm looking for comments and suggestions

Here's an exercise that I find amusing.

Consider the following apparatus
http://www.av8n.com/physics/img48/block-on-fall.png

This is called a "block on fall". Note that "fall" is an old
term for the rope in a block and tackle, and hence "block and
fall" is another name for block and tackle. Here we have
attached a secondary block and fall (rigged with green rope)
to the hauling part of the primary block and fall (rigged
with black rope). The attachment is made using the short
red rope to make a Magnus hitch around the black rope.

The user hauls on the hauling part of the green rope, shown
as the free end near the center of the diagram.

Also note that if the primary and secondary are "luff
tackles" (which these are not), this apparatus is called
luff on luff, or luff upon luff. Sometimes the latter
name is extended to include the case we have here, but
in all cases I prefer the more descriptive name: block
upon fall.

The purpose, of course, is to lift a heavy object (shown in
black). The object was initially near the bottom of the diagram,
so it has already been lifted quite a bit to reach the position
shown in the diagram.

1) Calculate the overall mechanical advantage of the system.
For simplicity, you may neglect friction.

2) Near the middle of the bottom of the diagram, the black
rope is shown cleated. What is the purpose of this?

3) Explain why a block-upon-fall might be sometimes more
practical than the obvious "direct approach" of building
a single block-and-tackle with the same mechanical advantage.

====================

Pedagogical and philosophical remarks:

I am stunned by the recent messages that suggest students
should "find the equation that applies" by scanning the
"list of equations". Maybe I'm reading into it more than
I should ... but IMHO, that sort of "equation hunting" is
not physics.

Let's be clear: I have no objection to writing down a list
of equations. My point is more subtle: In any problem that
involves real physics, i.e. /understanding/ the physics:
a) You will need to apply more than one equation.
b) It will not usually be obvious /how/ the equation applies.
That is, each equation must be applied in a somewhat indirect
fashion. You need to understand the problem ... and understand
the equations ... in order to figure out how to proceed.

The approach of "looking up the equation" the way you would look
up a word in the dictionary might work for a certain type of
cloyingly simple, artificial, "textbook" problems, but it cannot
be extended to real-world problems. Indeed, it cannot even be
extended to the second semester of the introductory physics class
(unless the class is severely dumbed-down).

In the case of the block-upon-fall, I can tell you all the equations
and all the principles that apply. There's nothing tricky about
any of that. However, that still leaves you with the main part
of the task: Figuring out /how/ the equations apply.

Also note that part (2) and part (3) are qualitative conceptual
questions. There is no equation that you can plug-and-chug to
answer these questions. There are equations that apply, but
you need to understand what these equations /mean/ in a practical
situation in order to answer the questions.

Like most real-world problems, this is a "story problem". The
students need to be able to cope with story problems at the high
school Algebra I level. (Supposedly that is a prerequisite for
the physics course, but we all know how little that means.)

This exercise has a property that is not necessary but is
nevertheless common and somewhat noteworthy: if you understand
what is going on, you can answer the question instantly. So
in some sense it is an easy problem. On the other hand, if
you don't understand what is going on, no amount of plugging
and/or chugging is going to help. You will not get an "E"
for effort.

==========

It's easy enough to set up a hands-on demonstration of block
upon fall. It's not quite as practical as a modern chain
hoist, but it definitely works. Forsooth it works so well
that you might want to think twice about the safety issues;
you can easily develop enough force to break things.
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