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

[tamtam402]

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?

I'm having trouble visualizing these things.

Thanks!

 

[Nugatory]

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.

 

[tamtam402]

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.