What components would I need to build a basic circuit that completes when something is pulled with a certain amount of force?
Not sure what your mechanical requirements are, but if you can afford some movement when the rope is pulled, go with DKNguyen's recommendation of using a linear spring with a contact at the spring deflection distance that indicates your "Y newton" point.

Green is insulation and orange is conductor (supposed to look like copper, eh) so you can trim your insulation at whatever length will give you the desired "d" distance based on the linear equation for springs:

\begin{equation}
Force = Spring Constant * Distance
\end{equation}



In actual implementation you'll want a way to reliably hold the wire against the rounded contact and prevent corrosion if left outside.

You can also measure it remotely with a water filled syringe. Attached the plunger to the rope/spring interface and the body of the syring to the fixed end of the spring. Run tubing to a safe area and use another syringe with a limit switch or an open vessel with a float switch.

Lastly, if you can't afford motion or need more accuracy, you can use a load cell. You could measure the pull of the rope directly using an S-type load cell like a cheap one scavenged from a hanging luggage scale. You could also use a flat load cell and compress it using a Class 1 lever, this would also give you flexibility to use the cheapest 1/2/5/10 kg cell you can find and adjust the lever arm for the force range you expect to measure. Either way, you could use a wheatstone bridge to set a threshold and trigger a response or use an ADC to read the load cell digitally with a microcontroller if you need to get actual numbers from the sensor.

For the variable resistance stretching cord that OP found:







simulate this circuit &ndash; Schematic created using CircuitLab