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Homework Statement
The problem is that using a human powered bike-like machine we have to climb up a 16 meter long rope. The total weight of the machine + human is 1300N and the theoretical force delivered by the human is 250 Newtons. The crank is 17cm long (that's the length of the arm, the radius of the gear is 11 cm). We are using a winch to climb up the cable. The winch has a radius of 3.1 cm. We now have to calculate the radius of the gear that has to be attached to the winch. The two gears will be connected with a bicycle chain.
After some research we came to the conclusion that we want to cycle at around 100 rpm.
Homework Equations
There's a bunch of ratio equations we used. They are really simple and i doubt they are necessary to put on here.
The Attempt at a Solution
The attempt is very very long. We took several approaches. We always end up with a smaller gear at the top (where the winch is) in contrast to the cranked gear. This kind of seems impossible to us since we are trying to get a light gear ratio where the cyclist doesn't have to push too hard to lift the entire system.
So we assumed that the input force would be 250 Newtons and the output would be 1300. What we did think of is that the crank is able to deliver a moment but we were unsure on how to include that in our calculations.
Ultimately we ended up with nothing.
This is a very old image of our concept, but the general idea is the same. (the chain is not included)