Need maximum weight on an extension machine

AI Thread Summary
To achieve maximum weight and resistance on a centered axis extension machine using a pulley system, it’s essential to consider the design constraints and desired resistance levels. Reducing the number of pulleys can increase resistance, but this may not be feasible depending on the machine's design. Lowering the attachment point of the cord towards the feet on the leg support can also enhance resistance. Visual aids, such as diagrams of the current mechanism, can help clarify the setup and potential modifications. Providing more specific details about the machine's design will facilitate better advice on optimizing resistance.
idontknoww
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TL;DR Summary: Need ideas on how to get maximum weight/resistance out of a pulley system in a centered axis extension machine

Hi so I am studying mechanical engineering and am currently working on a factory that makes gym machines, and I wanted to know if anyone could explain to me how I could get maximum resistance/weight with a pulley system. The only thing that comes to mind is using less pulleys, which I don’t think I can, and the second thing I thought of is putting the end of the cord lower towards the feet on the leg support thing (sorry don’t know the name of that). Helps a loooot if you could explain visually
 
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Welcome to PF.

idontknoww said:
Helps a loooot if you could explain visually
You can attach a picture of the existing machine mechanism to your next post.
There is an "Attach files" button at the bottom left of the reply window.
 
idontknoww said:
explain to me how I could get maximum resistance/weight with a pulley system.
Fix the rope to the floor.

Seriously tough, you need to be more specific about the design constraints and desired resistance.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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