A single movable pulley is supported by two rope segments. Explore how their angle changes the ideal vertical force ratio and the local relationship between rope movement and load rise.
Single Movable Pulley Ideal Geometry Calculator
Enter a local rope displacement and a symmetric segment angle from vertical. The worksheet reports the ideal vertical force ratio, tension fraction and work-consistent local load rise. It does not rate any real rope, block, anchor, hook or lift.
Equation Used
- One massless inextensible rope gives equal tension in both segments.
- Both supporting segments are symmetric at the entered angle from vertical.
- The moving block is in quasistatic vertical equilibrium.
- Friction, rope mass, bending, inertia, shock, hardware capacity and safety factors are excluded.
Two equal tensions support the moving block through their vertical components. The local displacement ratio follows the same geometry and assumes a constant rope angle.
Two equal rope tensions support the moving block
In the ideal massless-rope model, both segments have the same tension T. Their vertical components support the moving pulley and attached load. For symmetric segments at angle theta from vertical, equilibrium gives W=2T cos(theta).
At theta=0, both segments are vertical, the ideal force ratio is 2, and one metre of load rise requires two metres of rope displacement.
A force-and-displacement teaching model
This page illustrates the ideal geometry behind a single moving block. Real lifting-system selection requires rated hardware, configuration-specific instructions and qualified practice outside this calculator.
Symmetric ideal force polygon
Ideal vertical-segment example
With theta=0 and 2 m of rope displacement, MA=2, ideal tension is 0.5W and the load rises 1 m. At 45° in the local symmetric abstraction, MA=1.414 and 2 m of rope displacement corresponds to 1.414 m of local load rise.
Ideal geometry is not a rigging rating
The ideal force ratio does not determine the load capacity of a rope, block or anchor. Real lifting equipment must be selected for its actual configuration and rated capacity; friction and changing rope angles can also affect effort and movement.
Single movable-pulley questions
Why does angle reduce ideal force ratio?
Only the vertical component T cos(theta) of each segment supports the load.
Why does local rise change with angle?
Ideal work requires T s=W y, so y=s/[2cos(theta)] in the constant-angle local model.
Can this select lifting equipment?
No.
Movable-pulley references
- OpenStax College Physics 9.5, Simple Machines: equal rope tensions add and two supporting cables give ideal mechanical advantage approximately 2.
- OpenStax Physics 9.3, Simple Machines: ideal pulley advantage equals the number of supporting rope segments and input distance increases in the same ratio.
- NASA Mars Robotics Education Poster, Activity 7: a mechanical advantage of 2 halves ideal effort and doubles effort distance.
Building or designing a mechanism like this?
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