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Re: [Phys-l] Work and Energy: which first?



As Professor Denker says, it is a matter of taste. I like
this progression since it starts with easy equipment before
it gets to the black box stuff.

I start with a series of pulley activities, starting with a
simple pulley and advancing to compound ones. The string
arrangments are hard to describe in email. I show them how
to put them together in class and how to draw pictures of
the pulleys. You probably know them already.

The lesson is structured around a series of activities that
are the answers to questions. I will give you the questions
for the first few.

1. How much force does it take to lift Block A (and
pulley), if lifted slowly a distance of 10 cm?

Students measure this force with a spring scale.

2. How much force does it take to lift Block A a distance
of 10 cm using a simple hanging pulley?

Students attach the scale to the string and measure the
force and discover that the force is now approximately half
as much.

3. Does the scale need to be moved 10 cm to make the block
move 10 cm?

No. The scale has to be moved 20 cm to make the block go up
10 cm.

4. Using a single pulley and a double pulley (single pulley
on top and double pulley on the bottom with two loops), how
much force does it take to lift the block 10 cm?

5. Does the scale need to be moved 10 cm to make the block
move 10 cm?

6. If I use a double pulley and a triple pulley to raise
the block 10 cm, how much force will it take?

Only half of the students can make this prediction
correctly, but none are really surprised by the result.

7. How much does the scale need to be moved to make the
block move 10 cm?

Nearly every student has caught onto the pattern by now and
can successfully make this prediction.

We say that lifting the block requires something -- a force
and a distance that the force is applied. We notice that we
can reduce one, but only at the consequence of increasing
the other.

We decide to call this something work. (Actually, last year
we called it jake, but that's another story.) I am
particularly fond of these kinds of operational
defninitions.

We then follow a series of activities similar to this with
an inclined plane and a cart. Once again, we note that we
can reduce the force by changing the angle, but the
distance necessary to get to the top increases. The total
work stays the same. Even in the limiting vertical case,
the work stays the same.

We notice next that the cart at the top of the hill will
come rolling down to the bottom, gaining speed the whole
way. We measure this speed with a photogate and discover
that the speed is nearly the same for all lengths of ramp,
but different for all the different heights of the ramps.

We figure that somehow the work was stored in the cart at
the top of ramp. Since work, force x distance, was always
equal to the force times the height (in the pulley case)
and the force of a cart is m g, then the energy stored due
to the object's height is m g h.

We then take our measurements and try to find a formula
that relates the speed at the bottom with the energy due to
the object's height. We call this value kinetic energy. We
check this with a pendulum bob.

We use this formula for kinetic energy to find the formula
for Hooke elastic potential energy using a photogate and
the springs built into the Pasco Carts.

Marc "Zeke" Kossover
The Jewish Community High School of the Bay






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