Does a Double Pulley System Double the Stretch Distance of a Spring?

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In a double pulley system, the movement of the rope is twice that of the load, but this does not mean the stretch distance of a spring is also doubled. When visualizing the system with a spring or chain, half of the rope's length increase is used to accommodate the movement on the other side of the pulley. As a result, the load experiences only half of the total stretch distance of the spring. This understanding clarifies the mechanics of the system and aids in visualizing similar scenarios. The conclusion is that the load's movement is limited to half of the spring's stretch distance.
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I know in a double pulley system, the rope moves twice the distance of the load. What about a system such as this? Would the stretch distance of the spring be twice the moved distance of the load?

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I'm having trouble visualizing these things.

Thanks!
 
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tamtam402 said:
I'm having trouble visualizing these things.

Draw two pictures, one in which the spring is replaced with a length of chain one meter long and another in which the spring is replaced with a length of chain two meters long. Keep the length of the rope the same in the two pictures.

Compare them... You'll see the answer to your question pretty quickly, and forever after be better at visualizing these things.
 
Thanks. I think I see it now. Half of the "rope" (spring) length increase must be "used" to increase the length of the rope on the other side of the pulley. This other half of the length increase is not used to displace the system towards the bottom.

It follows that the load would indeed only see a y = <LengthIncrease>/2 movement towards the bottom. Sorry about the vocabulary used, I'm not a native english speaker.
 

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