This kind of stuff is in the first chapter of a basic course in "Static's".
With everything at rest there has to be a balance of Forces in both
Vertical and Horizontal directions. The tension on the rope is a function
of the angle ( from the horizontal) that it is being pulled at. The Vertical
Force to be balanced is the downward one of 40 lbs.
Since the weight is split between the two ropes the vertical force is 20 lbs
on each side. The tension of the rope (on each side) can be found by using
the equation:
Sin (angle)= (side opposite/hypotenuse), where the hypotenuse is the rope.
The vertical force (or side opposite) is equal to 20 lbs. since 20 +20=40
The tension on the rope is.
For an Angle=10 deg Tension=115 lbs; Angle 50 deg Tension=15 lbs; Angle =80
deg Tension=20.3 lbs: and if the angle is =90 deg the Tension would be 20
lbs in each side.
Doesn't it make sense that if the rope is nearly horizontal that you'd have
to pull like heck on it to hold up a weight. That's because most of your
pulling is in a horizontal direction and you'd need a very large force in
order to generate the vertical force needed to balance the weight.
MLD
"Tom Miller" wrote in message
...
On Thu, 11 Mar 2004 20:57:31 -0500, (The Other
Harry) wrote:
| [On 11 Mar 2004 07:41:35 -0800,
| (Harry K) wrote:]
|
| Wrong. The tension on both sides will be equal (20 lbs) and the
top
| hook will feel 40lbs. There is nothing being added to the 40 lbs
to
| increase it to 80. I think you have confused the effect of a
pulley
| which, when rigged right, will cut the lifting force by 1/2.
|
| This is what I think. I still do.
|
| I can see how where the the hooks are placed might make a
| difference, but I can't see how 40 pounds would ever go to
| 80. Not without something else happening.
|
| I'll test it.
|
| --
| Harry
If the pulley is fixed overhead and one is pulling on the end of the
rope passing over the pulley to lift the weight, it is exactly the
same as if you were standing overhead lifting the weight directly. It
is (in this case) 40 pounds either way. The weight of the object being
lifted using the first class pulley is not "split" into 20 lbs and 20
lbs. It is all one rope and all 40 lbs. The fact that you are using
the pulley merely changes the direction you have to pull. In some
cases this is more convenient, but the work and the weight is the
same.
To summarize:
The weight of the object is 40 lbs.
The weight on the rope is 40 lbs.
The weight on the hook is 40 lbs.
A first class pulley does not "split" the weight, nor does it give any
mechanical advantage. To raise the weight one foot, you pull the rope
one foot using 40 lbs of force.
If you were to attach the pulley to the weight, however, and tie the
rope overhead, and stand above the weight and pull on it, the lift
force on each side of the rope would be half the weight of the object
being lifted. You would have to pull with a force half as much as the
weight. In the example, the object weighing 40 lbs could be lifted
with a pull of 20 lbs of force. The other leg of the rope attached
overhead (above the weight) would be holding the other 20 lbs (the
ceiling holds 20 and you hold 20). You will have to pull the rope two
feet to raise the weight one foot. This is a 2:1 mechanical advantage.
If you add an additional pulley to the ceiling, you can now lift from
below, which is more comfortable. But you gain no additional
mechanical advantage beyond the 2:1 ratio.
However, if you add yet another pulley to the ceiling and run the rope
through it and then through the 3rd pulley (we now have one end of the
rope anchored, two ceiling pulleys, and one pulley on the weight) you
will then again halve the force needed to raise the pulley. Instead of
taking 20 lbs of force to raise a 40 lb weight, it now will take 10
pounds. Each segment of the rope now bears 1/4 of the weight but must
be pulled four feet to raise the weight one foot. The total weight on
the ceiling is still 40 lbs.
The problem everyone seems to be having is that there is no mechanical
advantage to using a first class pulley, so no force is shared. It is
the same as if you picked up the rope and lifted the weight directly
without using a pulley. There is only mechanical advantage -- shared
forces -- using the pulley attached to the weight, or using compound
pulleys such as in a block and tackle. Using the single pulley
attached to the ceiling, the force required is all on your side. The
weight cannot pick up or hold itself or half of itself -- or indeed
any of itself. The weight supported by the ceiling hook and pulley is
the full 40 lbs of the weight.
Here are some diagrams:
http://www.wcsscience.com/pulley/page.html
HTH.
If you guys had been paying attention in third grade instead of
throwing spitballs .... :-)