Potential Energy Transfer from a large mass to accelerate a smaller mass upward

[Fer137]

TL;DR Summary

Potential Energy Transfer from a large mass to accelerate a small one upwards.

With the potential energy of a large mass (for example 50 kg at 10 meters high) I want to accelerate a smaller mass (5-25 kg) upwards. I see that simple mechanisms like pulleys, levers, and simple gears leave a lot of kinetic energy in the large mass when it reaches the ground.
Is there some clever mechanism that optimally transfers the energy to the small one? Ideally with some combination of levers and/or gears. (Hydraulic or Pneumatic as a last option) How to optimally transfer potential energy from a large mass to accelerate a small one upwards.

 

[anuttarasammyak]

Accelerated small mass m has zero speed at the its peak height. To get this final state e.g. the both m and large mass M are at rest ;
1. Connect m and M with rope.
2. Prepare a triangle ABC with surface smooth material so that sin A / sin B = M/m and BC is fixed on the ground.
3. Put m on slope AB, M on slope AC, and the rope on a pulley at A.
M and m balance on the slopes. With infinitesimal energy we can make M down and m up with infinitesimal speed.

 

[Fer137]

Accelerated small mass m has zero speed at the its peak height. To get this final state e.g. the both m and large mass M are at rest ;
1. Connect m and M with rope.
2. Prepare a triangle ABC with surface smooth material so that sin A / sin B = M/m and BC is fixed on the ground.
3. Put m on slope AB, M on slope AC, and the rope on a pulley at A.
M and m balance on the slopes. With infinitesimal energy we can make M down and m up with infinitesimal speed.

A pulley with an inclined plane? Thanks, but that doesn't work. It's one of many possible examples where the large mass conserves much of its energy at the end of its path (kinetic), without transferring it to the mass that is going up.

 

[berkeman]

Welcome to PF.

Is there some clever mechanism that optimally transfers the energy to the small one? Ideally with some combination of levers and/or gears. (Hydraulic or Pneumatic as a last option) How to optimally transfer potential energy from a large mass to accelerate a small one upwards.

Yes, there are some ways that I can think of. But first, is this question for schoolwork? What is it for?

 

[gmax137]

Trebuchet

 

[jack action]

You might be interested in a stacked ball drop:

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[anuttarasammyak]

A pulley with an inclined plane? Thanks, but that doesn't work. It's one of many possible examples where the large mass conserves much of its energy at the end of its path (kinetic), without transferring it to the mass that is going up.

After potential energy is transferred from M to m, i.e. M goes down and m goes up, it is rather easy to transfer potential energy of m to its kinetic energy.

 

[Fer137]

Thanks everyone. I actually had some errors in the spreadsheet that underestimated the potential energy transfer. Fixed it for now.

Merry Christmas and Happy New Year.

 

[Fer137]

Welcome to PF.


Yes, there are some ways that I can think of. But first, is this question for schoolwork? What is it for?

Your question rejuvenates me:)