Hi, kids!
Welcome to a new weekly Science Lab video.
We’re moving on!
Let's continue to talk about simple machines.
In this case, the pulley.
A pulley is a wheel on an axle that is designed
to allow movement and change of direction
of a tight rope, cable, belt, or chain.
In reality, the mechanical advantage provided
by a simple pulley in itself only derives
from the change in the direction of movement.
For example, a pulley that hangs from above
allows a rope to be pulled down, turning it
into an upward force on the load.
Thus, we can use our entire weight as a pulling
force, which is itself a mechanical advantage,
but it doesn't spare you from having to apply
a force equal to or greater than the weight
of the load.
Pfff, what a rip-off!
I mean, okay, but... isn't there any way a
pulley can allow me to move very heavy objects
without hurting my back?
Of course there is!
Wait till I tell you.
There's a famous historical note on the usage
of the pulley by the Greek-Roman historian
Plutarch, who in his work Parallel Lives recounts
a scene where Archimedes proved the effectiveness
of pulleys:
In a letter to King Hiero of Syracuse, to
whom he had a great friendship, Archimedes
stated that with a given force he could move
any weight.
Hiero, being struck with amazement, asked
Archimedes to demonstrate.
They agreed that the object to be moved should
be a ship of the king's navy, for Hiero believed
that it could not be taken out of the dock
and put in dry dock without the use of great
effort and many men.
After loading the ship with many passengers
and with the holds full, Archimedes sitting
himself the while far off, with no great endeavour,
but only pulling a rope he lifted the ship
in a straight line without great effort, taking
it out of the water as smoothly and evenly
as if it were still at sea.
So the pulley is a simple machine, but not
for that reason any less formidable!
We only have to unlock the main secret of
pulleys to transform them into such powerful
devices: they can be movable.
If, instead of having the pulley fixed and
the weight hanging from the rope, we hang
the weight directly from the pulley, it will
behave differently, making the resultant force
double the force applied.
However, there is a price to pay, we will
have to pull the loose end of the rope twice
as far.
This is somewhat resembling the law of the
lever, isn't it?
On a moving pulley, the distance pulled is
twice the distance lifted, while the force
applied is half the resultant force.
This would allow you to lift loads that were
twice as heavy using the same force as with
the fixed pulley, or to lift a same load making
half of the effort than with the fixed pulley,
with the only downside being that you would
have to pull more of the rope.
Fantastic!
Right?
So fixed pulleys serve to change the direction
of the applied force, while movable pulleys
also multiply the resultant force at the cost
of making you pull more on the rope.
Quite easy.
By assembling many pulleys together something
called a block-and-tackle system is formed
in order to provide mechanical advantage to
apply large forces.
The more pulleys are assembled, the longer
the distance to be pulled, but also the larger
the resultant force compared to the force
applied.
This is what is known as a compound pulley,
hoist, or, more classically, polyspaston.
As always, the work on each side of the pulley
has to be the same.
Mathematically, it is expressed this way:
FA*lA=FR*lR
To better understand the effect of movable
pulleys, let’s define n as the number of
times the rope goes up and down in the pulley
system.
FA=FR/n
lA=lR*n
Therefore, we can say that the force needed
to lift a load with a simple fixed pulley
is the same than the weight of the object
because, in that case, n=1.
But in a simple movable pulley, n=2, and that’s
why the applied force is half the weight of
the load.
On the other hand, it can also be understood
in this way why the distance pulled is twice
the distance the load is lifted, in the case
of a movable pulley.
With these formulas, the values of both forces
and both distances could be calculated for
any pulley system by simply establishing what
the value of n is.
Let’s test it on our own!
Roll up your sleeves, for it’s experiment
time!
On this occasion, I have thought it would
be kind of hard for you to find examples of
pulleys in 
your houses, so I am going to show with this
interactive simulation that I 
am attaching to 
the task.
I am also attaching a video tutorial so that
you can make your own homemade pulleys and
experiment with their full potential with
your own hands.
In either case, building your own pulley systems
or using the simulation, test the effects
that we have been talking about.
Do the math to demonstrate it mathematically!
I hope you enjoyed this activity.
See you!
