Hi I'm wondering if you could briefly describe how pulleys work. I believe they create mechanical advantage. What are the important things to remember with pulleys. Thank you

First of all, thanks for continuing to utilize this forum! We're always here to help and love to see engaged students. You're right by stating that pulleys create mechanical advantage! This is their entire dedicated purpose.

As you've most likely put together from real-life experiences, pulleys make lifting heavy objects much easier by allowing the force required to be reduced. There is a decent amount to know about pulleys, but I can pretty much guarantee that this will cover everything you'll need to know. We'll discuss three important things:

The effort required to pull a load will be reduced by a factor 1/n related to the number (n) of pulleys.

The effort distance will be given by the load distance multiplied by this same variable n.

The mechanical advantage can be quantified by something called the efficiency.

Throughout this discussion it will be most important to recall the following equations for force (F) and for work (W), or change in gravitational energy:

F = ma,where m is the mass of the object and a is the acceleration (or F = mg assuming that g is acceleration due to gravity), and

W = mgh(where h is in this case the change in vertical displacement, or change in height).

It will also be helpful to refer to this image:

In a simple ideal pulley system (ideal meaning the usual: no energy lost to heat, friction, air resistance, etc.), a continuous rope is run through the wheel and attached directly to the load. In this case of system 1 above, there is technically no mechanical advantage, apart from the circumstantial convenience of being able to pull on the rope from any direction and lift the load vertically upward. This is still pretty helpful for certain situations! But there's not much else to know here. Regardless, a pulley will always be used to changed the direction of translational motion! This is part of the definition of a pulley.

In system 2, this rope is run through a second pulley. If you were to imagine a simplified free-body diagram, where the force of the load is translated directly 1:1 to the lower pulley (some books might refer to this as the "tackle"), the system might look something like this:

Notice that the force F = mg is equally distributed onto each of the two vectors T1 and T2. What does this practically mean? For any system that looks like system 2, the force required to lift the object F = mg will be halved. By extension, you can imagine a similar force body diagram for systems 3 and 4. In system 3 there will be a T1, T2 and T3 vector, meaning that the weight of the load will be divided by 3 and the force required to move the load will be one third of mg. In system 4 there is a T1, T2, T3 and T4 vector, the weight of the load will be divided by 4, and the force will be 1/4 mg. Can you guess the trend if there was a system 5 or system 6? This is one of the most important things to remember!

The truth is that systems of pulleys can get very complex and lift incredible amounts of weight. This might seem like some kind of magical hooey. There's an old legend from around 200 B.C.E. that the philosopher Archimedes once flexed pretty hard on the king of Syracuse by towing his largest, fully loaded 150 foot trading ship to shore with nothing but his bare hands (and, of course, a pulley system). History is rife with stories of early scientists showing off.

But pulleys do have their disadvantages! A certain law of physics states that the change in energy (or work) must be conserved. While the force required to lift a load may decrease by some factor 1/n (where n is given by the number of pulleys, or connections of the continuous rope to the load), the amount of energy must remain constant.

Let's say we're looking at system 4 again. If the pulley is able to raise the load 1 meter, the length of continuous rope in the pulley system (which crosses over this distance 4 times), must actually move a distance of 4 meters. This means that whomever is pulling that single length of rope on the opposite side of the pulley has to pull through 4 meters just raise the load 1 meter. This "4 meters" is referred to as the effort distance. The 1 meter that the load moves is called the load distance. The advantage here is that the force required is still only 1/4 of the force exerted by gravity on the actual load. Most people can pull that rope 4 meters, but they certainly might not be able to pull 4 times that weight! This is basically the textbook, formal meaning of mechanical advantage. Just like force, this rule can be generalized. For system 3, someone will have to pull 3 timesload distance. For system 2, the effort distance is 2 times the load distance. Etc. etc.

Lastly, you may see textbooks or exercises referring to mechanical advantage by quantifying it as an efficiency (E). The following formula is worth memorizing:

Load is the force mg on the actual load. Effort is the force which someone has to exert on the opposite end. Remember that this is always reduced by an integer factor n determined by the number of pulleys!

One last thing! The caveat with efficiency is that we're dealing with an ideal system here, in which we've discounted friction and the mass of the pulley system. In actuality, no physical system will have 100% efficiency. There are a number of factors that we call "negligible" and ignore when working with ideal models because the reality is so much more mathematically complicated. However, these ideal models serve to provide very accurate estimations. Common non-ideal factors for any system, but especially pullies, include energy lost to friction of the rope with the pulleys via heat (ever get a rope burn?), friction and resistance within the pulley rotating around its axle, and the actual mass of the pulley system itself (which, for some of these systems, can be quite heavy!). To a lesser extent forces like air resistance, changes in altitude and therefore variation in g will also result in experimental error from the ideal system. Essentially all of these non-ideal variables will result in a greater effort required to lift the load, thus decreasing efficiency.

Thanks again for posting on this forum. I understand this might have been a bit of a run-on, but again, I'm confident this should cover most of the important things that you need to know. Please feel free to ask for clarification on anything, or for worked examples. And remember that we're offering two upcoming Zoom Physics Tutoring sessions: one with Terra Marie Jouaneh on Wednesday, May 6, and another with Mohammed Chaghlil on Wednesday, May 13th!

Again, if you have more questions, please let me know!

Hello alvino.malik33,

First of all, thanks for continuing to utilize this forum! We're always here to help and love to see engaged students. You're right by stating that pulleys create mechanical advantage! This is their entire dedicated purpose.

As you've most likely put together from real-life experiences, pulleys make lifting heavy objects much easier by allowing the force required to be reduced. There is a decent amount to know about pulleys, but I can pretty much guarantee that this will cover everything you'll need to know. We'll discuss three important things:

The

effortrequired to pull aloadwill be reduced by a factor1/nrelated to the number (n) of pulleys.The

effort distancewill be given by the load distance multiplied by this same variablen.The mechanical advantage can be quantified by something called the

efficiency.Throughout this discussion it will be most important to recall the following equations for

force (and forF)work (, or change in gravitational energy:W)whereF = ma,mis the mass of the object andais the acceleration (orF = mgassuming thatgis acceleration due to gravity), and(whereW = mghhis in this case the change in vertical displacement, or change in height).It will also be helpful to refer to this image:

In a simple ideal pulley system (

idealmeaning the usual: no energy lost to heat, friction, air resistance, etc.), a continuous rope is run through the wheel and attached directly to the load. In this case ofsystem 1above, there is technically no mechanical advantage, apart from the circumstantial convenience of being able to pull on the rope from any direction and lift the load vertically upward. This is still pretty helpful for certain situations! But there's not much else to know here. Regardless, a pulley will always be used to changed the direction of translational motion! This is part of the definition of a pulley.In

system 2, this rope is run through a second pulley. If you were to imagine a simplified free-body diagram, where the force of the load is translated directly 1:1 to the lower pulley (some books might refer to this as the "tackle"), the system might look something like this:Notice that the force

F = mgis equally distributed onto each of the two vectorsT1andT2. What does this practically mean? For any system that looks likesystem 2, the force required to lift the objectF = mgwill be halved. By extension, you can imagine a similar force body diagram for systems3and4. In system 3 there will be aT1,T2andT3vector, meaning that the weight of the load will be divided by 3 and the force required to move the load will be one third ofmg. Insystem 4there is aT1,T2,T3andT4vector, the weight of the load will be divided by 4, and the force will be 1/4mg. Can you guess the trend if there was asystem 5orsystem 6?This is one of the most important things to remember!The truth is that systems of pulleys can get very complex and lift incredible amounts of weight. This might seem like some kind of magical hooey. There's an old legend from around 200 B.C.E. that the philosopher Archimedes once flexed pretty hard on the king of Syracuse by towing his largest, fully loaded 150 foot trading ship to shore with nothing but his bare hands (and, of course, a pulley system). History is rife with stories of early scientists showing off.

But pulleys

dohave their disadvantages! A certain law of physics states thatthe change in energy (or work) must be conserved.While the force required to lift a load may decrease by some factor1/n (wherenis given by the number of pulleys, or connections of the continuous rope to the load), the amount of energy must remain constant.Let's say we're looking atload distance. For

system 4again. If the pulley is able to raise the load 1 meter, the length of continuous rope in the pulley system (which crosses over this distance 4 times), must actually move a distance of 4 meters. This means that whomever is pulling that single length of rope on the opposite side of the pulley has to pull through 4 meters just raise the load 1 meter. This "4 meters" is referred to as theeffort distance. The 1 meter that the load moves is called theload distance.The advantage here is that the force required is still only 1/4 of the force exerted by gravity on the actual load. Most people can pull that rope 4 meters, but they certainly might not be able to pull 4 times that weight! This is basically the textbook, formal meaning ofmechanical advantage. Just like force, this rule can be generalized. Forsystem 3, someone will have to pull 3 timessystem 2,the effort distance is 2 times the load distance. Etc. etc.Lastly, you may see textbooks or exercises referring to

mechanical advantageby quantifying it as anefficiency (. The following formula is worth memorizing:E)Loadis the forcemgon the actual load.Effortis the force which someone has to exert on the opposite end. Remember that this is always reduced by an integer factorndetermined by the number of pulleys!One last thing! The caveat with efficiency is that we're dealing with an

ideal systemhere, in which we've discounted friction and the mass of the pulley system. In actuality,no physical system will have 100% efficiency. There are a number of factors that we call "negligible" and ignore when working with ideal models because the reality is so much more mathematically complicated. However, these ideal models serve to provide very accurate estimations. Commonnon-idealfactors for any system, but especially pullies, include energy lost to friction of the rope with the pulleys via heat (ever get a rope burn?), friction and resistance within the pulley rotating around its axle, and the actual mass of the pulley system itself (which, for some of these systems, can be quite heavy!). To a lesser extent forces like air resistance, changes in altitude and therefore variation ingwill also result in experimental error from the ideal system. Essentially all of these non-ideal variables will result in a greatereffortrequired to lift the load, thus decreasing efficiency.Thanks again for posting on this forum. I understand this might have been a bit of a run-on, but again, I'm confident this should cover most of the important things that you need to know. Please feel free to ask for clarification on anything, or for worked examples. And remember that we're offering two upcoming Zoom Physics Tutoring sessions: one with Terra Marie Jouaneh on Wednesday, May 6, and another with Mohammed Chaghlil on Wednesday, May 13th!

Again, if you have more questions, please let me know!