# What is Pulleys: Definition and 381 Discussions

A pulley is a wheel on an axle or shaft that is designed to support movement and change of direction of a taut cable or belt, or transfer of power between the shaft and cable or belt. In the case of a pulley supported by a frame or shell that does not transfer power to a shaft, but is used to guide the cable or exert a force, the supporting shell is called a block, and the pulley may be called a sheave.
A pulley may have a groove or grooves between flanges around its circumference to locate the cable or belt. The drive element of a pulley system can be a rope, cable, belt, or chain.
The earliest evidence of pulleys dates back to Ancient Egypt in the Twelfth Dynasty (1991-1802 BCE) and Mesopotamia in the early 2nd millennium BCE. In Roman Egypt, Hero of Alexandria (c. 10-70 CE) identified the pulley as one of six simple machines used to lift weights. Pulleys are assembled to form a block and tackle in order to provide mechanical advantage to apply large forces. Pulleys are also assembled as part of belt and chain drives in order to transmit power from one rotating shaft to another. Plutarch's Parallel Lives recounts a scene where Archimedes proved the effectiveness of compound pulleys and the block-and-tackle system by using one to pull a fully laden ship towards him as if it was gliding through water.

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1. ### 2 pullies and 3 masses -Tension

Hi, If i have a system that consists of 2 pullies and 3 masses, what is the tension on each part of the string? I know that for 2 masses hanging on either side of a pulley, the tension is the same. But for 3 masses, and 2 ideal pullies(no friction) and inextensible string, is tension the same...
2. ### A pulley system with two pulleys and two suspended masses

For this problem, The solution is, However, how do they know the block B will move up and block A will move down? The masses of each are not given so could be the other way round if ##m_b > m_a##? Also how do they know that if block B moves up by 1cm, block A will move down by 2cm? Many thanks!
3. ### Pulleys and coordinates

I'm not really struggling with the question but the coordinate systems involved more so. So due to the modelling assumptions we know that the tension will be equal throughout the rope so we can use f = ma on each particle respectively and solve the resulting equation (as acceleration will be...
4. ### How does this system work? (Four pulleys and a rope lifting a mass)

I used the regular way of solving problems with pulleys. I tried to find the tension forces, which must be the same in the rope, but I get it wrong
5. ### Problem with two pulleys and three masses

I know that the tension from pulley B (T1) has to be equal the m*g of m1 for m1 to have acceleration = 0. But i can't figure how this works because the m2 is already heavier. And so the block(M) has to be negative weight?
6. ### System of two pulleys and three masses

I used m1=m2=15,0kg System: FBD: Note: I believe I have solved a) correctly and am more confused about b). a) I started with drawing the FBD. Knowing that the net sum has to be zero for the system to be at rest I used the left mass to find the tension on the rope: S1 = G1 = 15kg*9,81m/s2 =...
7. ### Forces on two different blocks with two pulleys

I don't know what to do as I know the forces acting on it but not the scalar like I just don't understand the question with two different pulleys I know the tension same everywhere
8. ### Accelerating pulleys (3 pulleys and 3 masses)

hi,i have this question : m1=3kg m2=6kg m3=20kg there is no friction between m3 and the floor. what is the acceleration of each block? my attempt is : the pulley that moves is moving downward at the acceleration of m3. so the system of m1,m2 is moving downward at the acceleration of m3, then i...

10. ### Two Pulleys, Two Strings and Two Blocks

Someone pls solve this. I've done it but I'm not sure if it's correct. Thanks!
11. ### B Relating displacements in a pulley system

> The set up: At left end, the rope is pulled down with a distance $dx_1$ by a force of constant magnitude $F$, the mass of $M$ is wrapping around by rope on the right and moves up by a distance $dx_2$ due to this. Problem: Find relate the two displacements. I thought of applying energy...
12. ### Why are these pulleys equivalent?

I have to apologize if the diagram is awful: I drew it for the sake of asking... I am analyzing the rope that is hanging the pulleys. From the diagram, the pulley at the left (let's call it L), has two objects with mass M at both ends. The pulley at the right (let's call it R), has an object...
13. ### A simple system of two masses and two pulleys

hey there, I am confusing what is the right answer to this system of mass, I solved it a couple of time and I got different answers. can you help me with that? I need to find the expression of the acceleration of the 2 masses. thanks a lot,Adam.
14. ### Masses on strings and pulleys (iWTSE.org)

I don't understand the working shown on the website (seen above). Firstly, they establish 'up' as the positive direction for acceleration, so A is +4 and D is -4. They create two points, P and Q, and set acceleration values for them. I understand that connected particles have the same...
15. ### Imminence of movement with movable pulleys

Answer: E My solution: 1) Load 2q: Y direction: $$T_1cos\alpha=mg + 2Eq$$ 2) Load q: Radial direction: $$T_2-\frac{Fel}{sen\alpha}-\frac{Fmag}{cos\alpha}-\frac{mg}{cos\alpha}=\frac{mv^2}{l}$$ $$T_2cos\alpha=\frac{Fel}{tg\alpha}+Fmag+mg+\frac{mv^2cos\alpha}{l}$$ 3) Stem connected to...
16. ### Equilibrium of concurrent forces -- 3 Pulleys and 2 Weights

Help, this one is completely different, the weird pulley is making it hard for me and I don't even know what to do with it and where to start. The answer is 185N but I want to know how.
17. ### Pulleys and a Belt, with friction and Torque

Torque on driver T = 2300N x .2m = 460Nm Torque on drum T=2300N x .6m T = 1380Nm Not sure how to calculate friction force on these...Do we have to assume a contact angle of 180 degrees if nothing is given or is that even required? Not sure what a free body diagram would look like for this.
18. ### Engineering Constrained Motion of 7 Masses and 3 Pulleys

How do you set the direction for this problem? Do you look at the motion of the block? If you set right positive, does that automatically makes upward motion positive? I set right as positive and up as positive for this problem. However, my answer was wrong. Textbook solution set right as...
19. ### 2 masses and 2 pulleys (Kleppner and Kolenkow)

For the official answer, I would appreciate an explanation as to why there's a division by 2 in the constraint equation for the total length of the strings, and why the way I wrote my constraint equation is incorrect.
20. ### Three balls and two pulleys

i tried with conservation of energy. ##E_i = 0 ## ##E_f = 2 m v^2 - 2mgh - 2mg(\sqrt{h^2 + l^2} - l) ## ## v = \sqrt{g(h - l + \sqrt{h^2 + l^2})} ## Is it right?
21. ### Two pulleys lifting a mass in parallel

if the ends P and Q are being pulled down with a uniform speed its acceleration is zero and hence the Tension in the string will also be zero and if this is the case which force will make the block of mass M rise? is this a fatal flaw in the question?
22. ### Block on a wedge connected to pulleys

if the tiny block moves downward by an amount x, the wedge should also move forward by the same amount x as they are connected by the same string whose length has to remain constant, (by differentiating it wrt time we get speed) hence I concluded that v1 = v2, but my book says otherwise what is...
23. ### I need some help with mechanical advantage (pulleys)

I'm wanting to get a winch for my truck for vehicle recovery, but they are expensive. I know if I get a couple of snatch block pulleys, I can get a "smaller" (and less expensive) winch. My problem is that I don't know if the cable and pulleys need to be rated at or above the winch capacity, or...
24. ### What's my mistake in this problem in dynamics involving pulleys?

Find the acceleration of block A and B, given that the mass of pulleys and strings are negligible.. I could see that the block B has gravity acting on it, therefore the gravitational force on the block ##B## is ##F_B = 5 g## and hence the acceleration is ##g##. From the pulley to which...
25. ### The figure represents a system composed of pulleys

The figure represents a system composed of two ideal fixed pulleys that support three masses A, B, and C of the same mass M, suspended by light and inextensible threads. Massor A is simultaneously suspended by two wires, one connected to massor B (wire 1) and the other to massor C (wire 2). We...
26. ### Using Effective Mass to find the accelerations of 3 masses connected by pulleys

Since 2nd pulley accelerates downward with the same acceleration of m1, and because the string around pulley has a constant length, it must be that a2=−a1+ar and a3=−a1−ar, where ar is the relative acceleration between the pulley and m2. From the above 4 equations, we are supposed to determine...
27. ### Three masses connected by pulleys

I know that if A moves down 1 unit b will move up square root of 2 and 1kg will moves up 2 unit
28. ### Question on pulleys force and rope pulling

I have a question about the following 33 and 34. For number 33 I think the answer is B because you have to life up against the force of gravity. While with A you have gravity helping you out. The correct answer is A but I am not sure how. for 34 I think B because you have an extra pulley so...
29. ### Two movable pulleys lifting a mass

I solved the last part of the previous question, But I got no idea how to start solving this question Like how the rope is being attached, is it attached to the inner disk or the outer one.
30. ### System with Pulleys and a Rope That Might Break

I tried to solve The system of torque as following. I labelled pulley one is the one in the left, and two as the one on the right. α=a/R t1=(-F+T1) R=MR^/2α. So -F+T=Ma/2 for pulley 2 (T1-T2)R=MR^2/2. So T1-T2=Ma/2 for The box T2-mg=ma add the last two equation, to get that T1-mg=Ma/2+ma...
31. ### Pulleys with Torque: Free Body Diagram Analysis

Free body diagram is below, but I have confusion about the tension. The tension on the block and pulley should always be the same by Newton third law. so T1=T1' and T2=T2'. Part B) The system is in equilibrium so net torque on each pulley is equal to zero. Therefore T1'=T2' and T2'=T3. Applying...
32. ### Belt and Pulleys - Centrifugal Forces

Hi. I assume that vector summation of the centrifugal forces acting on the belt, on pulley A and B, equals to zero. Is Centrifugal force on pulley A static or dynamic force? What would, hypothetically, happen if the sum centrifugal forces acting on the belt are not zero? Could some kind of...
33. ### 2 inclined plane problems, one with pulleys

For the a part of the first problem I did this: mgsinθ < µk*mgcosθ Sinθ < µk*cosθ Tanθ < µk so θ should be less...
34. ### What is the correct way to solve for weight on two pulleys?

I've done this exercise twice now, the answer is 1.4m/s but I get 1.64m/s. It's too far off to be rounding error. 1. I don't use energy consideration, because I don't have a clue how that would work. 2. I still need to know what's wrong with my current way of solving this. Any help is...
35. ### Atwood System - max. height of the lighter object

Magnitude of acceleration of system: a = (4.59kg - 1.71kg)(9.81N/kg)/(4.59kg + 1.71kg) = 4.48 m/s^2 Velocity of lighter mass when heavier one hits the ground: vf^2 = vi^2 + 2ad = 0 + 2(4.48m/s^2)(2.60m) vf = 4.83 m/s [up] I am not sure what to do from here? I don't really understand what...
36. ### Calc Forces on Pulleys: 200N, 300N Masses, No Friction

Homework Statement: In Figure 3-25, the weights of the objects are 200 N and 300 N. It is considered that the pulleys have no friction and that their masses are negligible. Pulley P1 has a stationary axis, the P2 pulley can raise or lower freely. Calculate the tensions FT1 and FT2, as well as...

38. ### Dynamics: A wedge, a mass, and two pulleys

Problem Statement: In the arrangement shown in the figure, a block of mass m=2kg lies on the wedge of mass M=8kg.Find the initial acceleration of the wedge. Assume pulleys and thread massless and surfaces smooth. Relevant Equations: FBDs
39. ### Unraveling the Mystery of Pulleys: Understanding Force and Distance Ratios

So, there are is a type which I couldn't understand. 1: (I don't know this type name is, so tell me please) So, the books says if you push the rope, you will double your force, but instead, for every x distance you push, it will go x/2 distance(their work is the same), which I couldn't...
40. ### Solving for acceleration of two blocks with two pulleys

Equation 1: T = Ma1 Equation 2: mg - 2T = ma2 Equation 3: a1 = 2a2 Since a1 = 2a for equation one I get T = 2Ma1 mg - 4Ma1 = ma1 mg = 4Ma1 + ma1 mg = 4a1(M+m) a1= mg / 4M+m Not sure if this is correct. Can someone please help to make sure I'm doing this right? Thanx
41. ### Mass hanging from a 2-pulley system

Homework Statement I have a question about the pulley problem in the attachment. Homework Equations This question can be answered using equilibrium of forces, namely Fx = 0 and Fy = 0. The Attempt at a Solution The answer key states that for the sum of the x-components, we should use the...
42. ### Motion of a system that has two masses and three pulleys

Homework Statement Homework Equations F = ma The Attempt at a Solution I couldn't draw the freebody diagram. There's this weight of mass m, which is mg, downwards from m and there's tension T to upwards. This T affects mass M in the +x direction, but how could i find out the normal force...
43. ### Automotive Torque formula to throw a mass with two pulleys and a belt

Hey guys What's is the formula to find the force(torque) to throw a mass in the air that is 500kg/m(3) with 2 pulley and a belt. Thanks
44. ### MHB Two pulleys

Hello there, i need some help on my homework. there's no given numbers that's why it's hard for me to answer this one. Two pulleys with radii r1 and r2 rotate at angular speeds of w1 and w2. if the pulleys are connected by a belt, show that r1/r2=w2/w1
45. ### Series of masses and pulleys

Homework Statement Sorry for bad english[/B] There is serie of mass and pulleys. We Know we have more than two masses. System is balanced.We take m(m<<1) from on of the masses and add to another one. a) prove all the masses except these two have downward accleration b) prove mass with heavier...
46. ### Velocity of mass with pulleys

Homework Statement Homework Equations xcxcxcxcxcxcxcxcxcxcxc[/B]The Attempt at a Solution My attempt: Let displacement of A be x m, Let displacement of B be y m, and Let displacement of C be z m. Step2: [/B]a+b+c+d=(a+x-y)+(b+x)+c+(d+z) 2x-y=-z Differentiating LHS and RHS components...
47. ### Complicated pulley system on an incline?

Homework Statement Under the action of force P the constant acceleration of B is 6 m/s^2 up the incline as in figure. For the instant when B's velocity is 3 m/s up incline, what is the velocity of point C? How do I solve this using constraints? [/B] Homework Equations For a pulley system ΣT.v...
48. ### Infinite pulleys problem, why doesn’t this technique work?

The problem statement can be seen here http://www.feynmanlectures.caltech.edu/info/exercises/infinite_pulleys.html Since each pulley is presumably massless, it must have no net force on it and so the tension of each rope is half of the one above it. If we let T be the tension acting on m0...
49. ### MHB Angular speed of 2 pulleys on a belt

The two pulleys connected by a belt have a radii of 15 cm and 8 cm. The larger pulley rotates 24 times in 36 seconds. a. Find the angular velocity of the small pulley in radians per second. b. Find the linear velocity of a point on the belt that connects the two pulleys in centimeters per second.
50. ### Newton's 3rd Law (Pulleys - 1)

Hi, I'm new here. Could someone provide some guidance on how to start this problem?