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In lugnet.off-topic.geek, Jon Palmer writes:
>
> Imagine for a moment that this is possible. The small pulleys would
> disengage and shoot away (or explode perhaps) from the cable just before the
> object hit them. This would correct the course of the object. ex: It was
> going left, now it's going up and to the right, on its way to the next
> pulley.
>
> Thoughts?
Great job on the .space page so far!
A few points first:
- in the absence of gravity, the force on the pulleys will only exist if the
object in tow is continuously accelerating. Remember, accelerating can mean
following a curved path as well as speeding up.
- with no friction in space, the momentum of the object will carry it past
the position of the first exploding pulley and swing it around the next
pulley like a pendulum. It won't move in a straight line to the next pulley.
Pulley #1:
Say the winch rapidly accelerates up to a constant rate. The object (I'll
assume it's a basket) in tow would rapidly accelerate in the direction of
the tension in the line. Then it would float weightlessly to the first
pulley, keeping pace with the rate that the winch reels in line. There
would be a force on the pulleys only during the rapid initial acceleration.
Pulley #2:
Once the basket passes the first pulley, it's momentum will try to carry it
in a straight line. But since the winch will continuously try to shorten
the line, there will again be a tension and a force on the remaining
pulleys. The basket will be pulled toward the next pulley, but won't move
directly toward it (sort of like an orbit). What happens at the next pulley
depends on it's distance and direction compared to the direction the object
is travelling. Riding in the basket through a zigzag course of pulleys 90
degree turns from one another could be unpleasant. I did some quick math
for this situation, and the angle in radians that the basket revolves around
the second pulley is equal to the ln(R/r), where R is the distance between
pulley #1 and pulley #2, and r is the radius of a pulley wheel.
Imagine this arrangement, a path with two 90 degree turns:
. w
x .
The "x" is the starting point, the bottom "." is pulley #1, the top "." is
pulley #2, and "w" is the winch. Once the basket passes pulley #1, it's
direction of motion is 90 degrees away from pulley #2. If the distance
between the pulleys is 25 times the radius of a pulley wheel, the basket
will swing around the second pulley and be moving directly away from the
winch when it reaches pulley #2, causing the pulley to explode. This would
make for a rather violent jerk on the basket when it starts moving back
toward the winch.
A series of pulleys at each sharp turn could help mitigate the acceleration
required to make drastic changes in direction. Or, the pulleys could be
arranged 550 pulley wheel radii apart, so the basket swings a full 360
degrees around the second pulley when it explodes, so the basket would just
feel a hiccup on it's way to the winch.
Jeff J
(sorry for not posting lately - I have had no time for building MOCs, and
feel shame. I have a lot of catching up to do.)
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Message is in Reply To:
 | | A space physics question
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| Imagine a winch pulling a rope or cable through a series of pulleys (horizontal) that are staked to the ground. The pulleys are arranged so that the rope makes a zig zag pattern on the ground. There is an object at one end of the cable, being reeled (...) (22 years ago, 28-Dec-02, to lugnet.off-topic.geek, lugnet.space)
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