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I'm working on a school project that requires us to build a compound machine with a mechanical advantage of 9. It should be able to lift a 10oz soup can three or more inches by using the weight of fifteen pennies. My machine consists of an inclined plane with a mechanical advantage of 3.16 (base is 12 in, height is 4 in), a travelling pulley system with a mechanical advantage of 2, and a wheel and axle system with a mechanical advantage ~3.

Here is my machine: Compound Machine Pic

The total mechanical advantage should be 19, but when I put the weights on the system, it turns out that I need 45 pennies to lift the can, which means my mechanical advantage is 3. I checked for sources of friction, but I couldn't find any of note. I could add a second pulley to increase the MA, but I'd prefer to fix the problem instead of implementing a patch-up solution. Any help would be greatly appreciated.

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  • $\begingroup$ When you do your calculations have you included the mass of the "trailer" you put the can in? It looks a bit solid.... $\endgroup$
    – Solar Mike
    Sep 24, 2017 at 21:56
  • $\begingroup$ @SolarMike I didn't think of that, thanks. But even with the mass of the trailer, wouldn't the (ideal) mechanical advantage still be enough to lift the can? $\endgroup$ Sep 24, 2017 at 23:29
  • $\begingroup$ You need 45 pennies to get it to move uphill. How many pennies for it to start rolling down the ramp? Put 44 pennies with the can high up the ramp, then start removing them. My bet is less than 19 will be left. Static friction under load tends to reach awfully high values. I bet your "ballpen bearing" is where things get stuck. $\endgroup$
    – SF.
    Sep 25, 2017 at 1:18
  • $\begingroup$ 'It should be able to lift a 10oz soup can three or more inches' - Empty the can! But seriously, mechanical efficiency can go to pot in a hurry in compound machines. The friction of the cart is unnecessary if you lift straight up. But now you probably need another compounding element. The pen axle of your differential wheel imparts a huge frictional torque because the pen has a diameter nearly as large as the spool. Use as small an axle/bushing as you can, the friction force will be about the same, but the torque is proportional to the axle radius. $\endgroup$
    – Phil Sweet
    Sep 26, 2017 at 1:10
  • $\begingroup$ @PhilSweet Thanks! I replaced the wheel with the lid of a coffee cup and the axle with a pencil, and it worked out great! $\endgroup$ Sep 28, 2017 at 9:35

2 Answers 2

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I have a few suggestions when it comes to managing forces:

  1. Try putting the angle of the ramp and the angle of the cord in the same value. This will reduce the force required to pull it up as the system will utilize the wheels. as i can see, the front wheels are up, therefore, the cables tend to lose force.

enter image description here

  1. Try putting the center of gravity of the object "in-line" with the cord so that no moment occurs. You can try putting the can down to lower its Center of Gravity.

enter image description here

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  • $\begingroup$ Please give us feedback so that we can improve our suggestions. :) Note that the center of gravity is for the whole system, not the can alone. $\endgroup$
    – Jem Eripol
    Sep 25, 2017 at 11:00
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It's not massively surprising that you have a lot of losses in something like this.

Compound pulleys always generate a lot of friction as you tend to have a lot of points of contact and the bearings are often a bit crude.

The first thing I would suggest is to make sure that all of the bearings area well lubricated, this should help a lot. Maybe try lithium grease or a PTFE lubricant.

I also suspect that a major source of friction is where the cord unwinds on the axle, substituting something like filament nylon fishing line should help a lot with that.

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  • $\begingroup$ I wouldn't be too concerned about friction between the cord and the axle, but the two "things" (I can't make out what they actually are!) that the cord slides through on the cart and on the front vertical plate look like they mght have a high friction coefficient. Try replacing them with proper small pulley wheels. The "bearings" for the main shaft with the cord wrapped round it look pretty crude, as well - get some proper bearings (e.g. intended for roller skates etc) which will take a lot of side force (from your strings) without much friction. $\endgroup$
    – alephzero
    Sep 24, 2017 at 21:55
  • $\begingroup$ @alephzero by "things" do you mean the pulleys? I tried to reduce friction by adding those on the front of the car and on the vertical pegboard. However, I noticed that the pulley attached to the front of the car spins, while the one attached to the vertical pegboard dosen't (the cord is rubbing on it instead of spinning). As for the wheel and axle, I think I would be able to buy bearings. But I'd prefer to recycle as many parts as possible, and I'm not sure how else I could attach the bearings to the wheel without gluing them. Is there another way to reduce friction in the wheel and axle? $\endgroup$ Sep 24, 2017 at 23:22

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