# I How pulley diameter affects forces?

Tags:
1. Apr 21, 2017

### Alok

Whether the diameter/radius of pulley affects the force required in lifting a weight?

2. Apr 21, 2017

### haruspex

You need to describe the set up in full detail.
Is it just the one pulley with a rope slung over it, weight suspended on one side and downward pull exerted on the other?

3. Apr 21, 2017

### Staff: Mentor

Physicists analyzing pulley systems often forget about the stiffness of the rope/cable. As the rope goes around the block, it must bend and unbend. The smaller the radius the more bending, and the more resistance.

Think of a 1 inch steel cable on a crane. If the cable bends 180 degrees around a 2 inch diameter block, or a 12 inch diameter block, the mechanical advantage is the same, and the friction on the axle is the same, but the bending/unbending resistance is very different.

My sailboat uses a 6:1 ratio mainsheet pulley system. The resistance is considerable even under zero load, because of the bending/unbending of the rope. To minimize that, I use a loosely braided rope specifically designed to have low stiffness resistance to bending.

Last edited: Apr 21, 2017
4. Apr 22, 2017

### Alok

Take any case where there is a pulley and it is not fixed one though.. So will it affect the amount of force required to lift weight.. Because as much I know it's the tension that decides.. But jst I was wondering if diameter of the pulley used will also affect or not?

5. Apr 22, 2017

### Alok

Thank you.. Got smthng new to think over.. But will it be applicable in case of ropes also or in low scale use!??

6. Apr 22, 2017

### Staff: Mentor

7. Apr 22, 2017

### haruspex

Any real pulley has some axial friction(a torque). Consider how the extra pull required on the cable to overcome this depends on radius.

8. Apr 22, 2017

### Andy SV

So the answer is yes there is an effect
A bigger pulley with the same rotational mass will have less bearing friction do to slower rotation at the same load and less friction of the rope do to less bending and unbending

9. Apr 23, 2017

### haruspex

As long as the weight of the pulley is small compared with the rope tension, it doesn't matter if the larger pulley weighs more
Of course, if you care about how quickly the load can be accelerated, you do have to worry about the increased moment of inertia of the larger pulley.
Sort of, but that's not how I'd say it. For a given frictional torque at the axle, the difference in tensions (pull side minus load side) can be smaller because the larger radius gives it greater moment. Equivalently, for a given movement of the rope, the larger pulley turns through a smaller angle, so less work is done against the frictional torque.

10. Apr 23, 2017

### Nidum

The deciding factors in practical design of pulleys for more demanding applications can be rope stress and rope abrasion . These depend on pulley size and also on the rope groove form .

11. Apr 23, 2017

### sophiecentaur

This is all about the difference between Mechanical Advantage and Velocity Ratio (other names for this are available). People always quote the Velocity Ratio, which is based on the Maths of the various radii and pulley numbers but the Mechanical advantage is what you actually get. It takes into account friction and 'dead weight'.
I remember we were taught Efficiency = MA/VR
Low efficiency is not always a bad thing - it accounts for why screws don't undo themselves from the wall and cars don't wind themselves down on the jack.