If you have ever
looked at the end of a crane, or if you have ever used an
engine hoist or a come-along, or if you have ever looked at
the rigging on a sailboat, then you have seen a block and
tackle at work. A block and tackle is an arrangement of rope
and pulleys that allows you to trade force for distance. In
this edition of How Stuff
Works we will look at how a block and tackle works,
and also examine several other force-multiplying devices!
Understanding the Block and
Tackle Imagine that you have the arrangement of a
100 pound (45.4 kilogram) weight suspended from a rope, as
shown below:
In the above figure, if you are going to suspend the weight
in the air then you have to apply an upward force of 100
pounds to the rope. If the rope is 100 feet (30.5 meters) long
and you want to lift the weight up 100 feet, you have to pull
in 100 feet of rope to do it. This is simple and obvious.
Now imagine that you add a pulley to the mix, as shown
below:
Does this change anything? Not really. The only thing that
changes is the direction of the force you have to apply to
lift the weight. You still have to apply 100 pounds of force
to keep the weight suspended, and you still have to reel in
100 feet of rope in order to lift the weight 100 feet.
The following figure shows the arrangement after adding a
second pulley:
This arrangement actually does change things in an
important way. You can see that the weight is now suspended by
two ropes rather than one. That means the weight is split
equally between the two ropes, so each one holds only half the
weight, or 50 pounds (22.7 kilograms). That means that if you
want to hold the weight suspended in the air, you only have to
apply 50 pounds of force (the ceiling exerts the other 50
pounds of force on the other end of the rope). If you want to
lift the weight 100 feet higher, then you have to reel in
twice as much rope - 200 feet of rope must be pulled in. This
demonstrates a force-distance tradeoff. The force has been cut
in half but the distance the rope must be pulled has doubled.
The following diagram adds a third and fourth pulley to the
arrangement:
In this diagram, the pulley attached to the
weight actually consists of two separate pulleys on the same
shaft, as shown on the right. This arrangement cuts the force
in half and doubles the distance again. To hold the weight in
the air you must apply only 25 pounds of force, but to lift
the weight 100 feet higher in the air you must now reel in 400
feet of rope.
A block and tackle can contain as many pulleys as you like,
although at some point the amount of friction in the pulley
shafts begins to become a significant source of resistance.
Other Force/Distance
Tradeoffs You come into contact with force/distance
tradeoffs in all sorts of simple machines. For example, a
lever is an example of this phenomena:
In this diagram a force F is being applied to the left end
of the lever. The left end of the lever is twice as long (2X)
as the right end (X). Therefore on the right end of the lever
a force of 2F is available, but it acts through half of the
distance (Y) that the left end moves (2Y). Changing the
relative lengths of the left and right end of the lever
changes the multipliers.
In this diagram the left-hand gear has twice the diameter
of the right-hand gear. For every turn of the left-hand gear,
the right-hand gear turns twice. If you apply a certain amount
of torque to the left-hand gear through one rotation, the
right-hand gear will exert half as much torque but will turn
two revolutions.
Another good example is a simple hydraulic system, as shown
below:
Assume that you have two cylinders full of water with a
pipe connecting the two cylinders together as shown. If you
apply a force F to the left-hand plunger, it creates a
pressure in the left-hand cylinder. Let's say you apply a 10
pound downward force to the left-hand cylinder. Let's also say
that the radius of the left-hand cylinder is 0.57 inches.
Therefore, the area of the left-hand piston is Pi * 0.57 *
0.57 = 1 inch. If the radius of the right-hand cylinder is 4
times greater, or 2.28 inches, then the area of the right-hand
piston is 16 inches, or 16 times greater. If you push the
left-hand piston down through 16 inches with a force of 10
pounds, then the right-hand piston will rise 1 inch with a
force of 160 pounds. Hydraulic cylinders of all sorts take
advantage of this simple force-multiplying effect every day.
You can see that a block and tackle, a lever, a gear train
and a hydraulic system all do the same thing: they let you
magnify a force by proportionally diminishing the distance
through which the magnified force can act. It turns out that
this sort of force multiplication is an extremely useful
capability! Here are some of the devices that use these simple
principles:
In this diagram, the pulley attached to the
weight actually consists of two separate pulleys on the same
shaft, as shown on the right. This arrangement cuts the force
in half and doubles the distance again. To hold the weight in
the air you must apply only 25 pounds of force, but to lift
the weight 100 feet higher in the air you must now reel in 400
feet of rope.
