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5.6Simple Machines: The Pulley
Even the most complex machines, such as cars or pianos, are built out
of certain basic units called simple machines. The following are some of the
main functions of simple machines:
transmitting a force: The chain on a bicycle transmits a force from the
crank set to the rear wheel.
changing the direction of a force: If you push down on a seesaw, the
other end goes up.
changing the speed and precision of motion: When you make the
“come here” motion, your biceps only moves a couple of centimeters
where it attaches to your forearm, but your arm moves much farther
and more rapidly.
changing the amount of force: A lever or pulley can be used to increase
or decrease the amount of force.
You are now prepared to understand one-dimensional simple machines,
of which the pulley is the main example.
Example: a pulley
Question: Farmer Bill says this pulley arrangement doubles the
force of his tractor. Is he just a dumb hayseed, or does he know
what he’s doing.
Solution: To use Newton’s first law, we need to pick an object
and consider the sum of the forces on it. Since our goal is to
relate the tension in the part of the cable attached to the stump to
the tension in the part attached to the tractor, we should pick an
object to which both those cables are attached, i.e. the pulley
itself. As discussed in section 5.4, the tension in a string or cable
remains approximately constant as it passes around a pulley,
provided that there is not too much friction. There are therefore
two leftward forces acting on the pulley, each equal to the force
exerted by the tractor. Since the acceleration of the pulley is
essentially zero, the forces on it must be canceling out, so the
rightward force of the pulley-stump cable on the pulley must be
double the force exerted by the tractor. Yes, Farmer Bill knows