# What is Pulley: Definition and 1000 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. ### Absolute motion analysis of pulley-spring system

Hello! I have this problem from an old exam I'm trying to solve. The problem is in Swedish so I've translated it: NOTE that I accidentaly wrote $$C\neq 1$$ in the picture below. The correct problem statement is above. But that part is not what I have problems with. The answer key says "if the...
2. ### Confused about how forces in a pulley balance

The question is regarding this image, I understand the two 50N forces provide a clockwise moment of 40 x 10^-2 x 100 which gives option D, as this moment must be balanced by the moment given by T. Now my question is, how is the net force on this system equal to 0? It says it is in equilibrium...
3. ### How Does a Pulley System Affect Scale Readings?

A kid is standing on a scale and holding a rope that goes through a pulley, on the other side the rope is connected to a spring and then to a 50N mass item. Assume that the kid's weight is 700N 1. While in static mode - what will the scale show? 2. The kid is now pulling the rope to get the mass...
4. ### How Do Pulleys Multiply Force in Complex Systems?

many pulleys at various angles multiply the initial power of the winch
5. ### Solving a Non-Equilibrium Pully System with a Fixed Length Rope at a 154 Degree Angle

Please note that the system is not in equilibrium, and that tension must be solved for the instant where the angle is 154 degrees. My attempt (correct ans is Ft = 626N)
6. ### Pulley system with equal spacing

Dear readers, I want to design a pulley system like in the schematic below, a system where the distance between certain attachment points are equally spaced along a vertical bar. The main feature of these pulleys is that when a force (F) is applied on one end of the cable, the attachment...
7. ### Work Pulley Problem with constant speed

For A the 1.2 kg block is being pulled by gravity hence work is done downwards which will make work positive since it's going with the same direction as the force. 1.2 * 9.8 = 11.76 N pulled downwards Work = F*d 11.76*0.75 = 8.82 J The tension is the other force and since the thing is...
8. ### Find the man's tension pulling the rope

The elastic force of the board,N=G_1+G_2=1000N. The kinetic friction f=μN=200N. The tension T=f=200N.
9. ### Tension Question with One Mass and Two Pulleys

My question is how come the tension in pulley 2 is pointing downwards. I was under the impression that tension always points away from the mass.
10. ### If tension provides the torque to this pulley, what is its equation?

15 - Tension = 1.53*a T = 15 - 1.53*R*α T*0.33 - 1.10 = Iα Is this approach correct?
11. ### I Pulley question -- Three pulleys lifting a mass...

Hi, I have this pulley question, i have to find the force F that needs to be applied to the string to keep the system in equilibrium. I found 150N. Is it correct? T_1= 300N and T_2=150N so F is 150N.
12. ### MIT OCW 8.01 PS10.6: A Massive Pulley and a Block on an Incline

Set up the force equations: (1) ##mgsin(\beta) - T = ma_{1}## (2) ##TR = I_{s}\alpha_{1}## Multiply (1) by ##R## and isolate ##TR##: ##R(mgsin(\beta) - T) = R(ma_{1})## ##mRgsin(\beta) - TR = mRa_{1}## ##TR = mRgsin(\beta) - mRa_{1}## Plug ##TR## into (2): ##TR = I_{s}\alpha_{1}##...
13. ### Finding acceleration of the pulley block system

What is the initial acceleration of mass 5M .The pulleys are ideal and the string inextensible. My attempt- 2Mg-T=2Ma (for 2M) T=Ma (for M) Solving we get T=2Mg/3 T-N=5MA (for 5M) N=2MA (for 2M) Solving we get A=2g/21 but the given ans. is 2g/23
14. ### Block and pulley on movable incline

This was the question: I derived the equations as mentioned in the relevant equations. But I could not solve the equations to find the answer. I realise with respect to inclined plane the acceleration must be a since string cannot slack. With respect to ground, the acceleration of incline is...
15. ### Net Torque Within a Mass and Pulley System

I started by summing the forces and torques to get: - ma = mg-T - I*alpha=Tr I then used a=alpha*r and I=Mr^2 to combine the equations and solved for angular acceleration equals 81.75rad/s^2. Plugging this back into a torque equation I got that the net torque is 1.04Nm. However, the problem...
16. ### Angular acceleration problem for a pulley used to raise an elevator

I tried to multiply 1/8 g (1.22625) by the radius (1.25 m) and got 1.53 rad/s^2. This is actually the linear acceleration of the elevator. How do I get the angular acceleration of the disk? Thanks!
17. ### 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!
18. ### Pulley, two masses and an incline

For this problem, Why is the tension on each side not equal? For this problem I think the only assumption is that the string is inextensible so the accelerations of the masses are equal. Many thanks!
19. ### Pulley with friction, how to get the friction in the pulley?

First, I assumed that the tension in the rope connected to the block A equals the static friction ##\sum{}^{} F_x =0 \rightarrow T=N_A*0.5=100N##, then the W weight or force equals to the tension in the pulley and the tension T ##W=100+\frac{2W}{\pi} \rightarrow W=275.2N## It's the first problem...
20. ### Experimental Design: Pulley and Mass Hangers

^ This is my personal drawing of the diagram, I couldn't take a picture of the actual one. The setup is a pulley wrapped with a cord and mass hangers attached to each end. My first thought when approaching this problem was to first determine the rotational inertia of the pulley, then use some...
21. ### Engineering Determining Force and Directions on Truss with Pulley

So far I have used methods of joints to determine the forces at point E, D, and C. However, there is also a pulley attached to point D and E which I included in the sum of forces, but I'm not sure if that's the correct way to apply them. Every force I've calculated so far has also been in...
22. ### 3 pulley problem with attached masses

in the opposite problem that has three pulleys and two masses, the book is asking for : 1- the tension on the string. 2- the acceleration of pulley p1. 3- the acceleration of mass m2. 4- what should the mass "m" be such that m1 does not accelerate? note : pulley p1 has mass m, in the diagram of...
23. ### How to Determine Over-Amperage on Pulley Size Change?

I have a VPB-808 Fan (rated 4100 RPM) from Viron. I am currently trying to pull 1300 CFM at 7" SP, which needs ~2668 RPM (2.85 HP). I have a pulley drive motor (Baldor, EM3611T, 3HP, rated 1760 RPM, 4.2A). It is drawing about 2.8A with the following configurations. It is currently only blowing...
24. ### Hanging mass on a massless pulley

I have a conceptual question about this problem. I can write the 3.5 kg block equation as Fnet(block 1)=(Force of tension)-(Force of friction)=m1a I can write the 2.8 kg block as Fnet(block 2)=(Force of tension)-(Force of gravity2)=m2a My question is this If I set the forces of...
25. ### A 4kg mass sits on a frictionless table....

I got 13N but is that right because apparently, it's wrong Here's my work: F = mg = 2(10) = 20N F = ma a = F/m = 20/4+2 = 20/6 = 10/3 = 3.3m/s^2 T = mg - ma T = (2kg)(10m/s^2) - (2kg)(3.3m/s^2) = 13.4 N I appreciate it! And if I'm wrong could you show how you got your answer? Thanks
26. ### 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?
27. ### 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 =...

29. ### Mystery of a Tensioned Rope Split in Two Places

I'm attempting to repair my Ergotron Workfit station. After taking apart, I discovered the problem. A single nylon rope split, releasing the spring's tension. Because it is past the warranty, the manufacturer is recommending I toss the whole assembly and buy a new \$650 one. Doesn't seem the...
30. ### Engineering Pulley system with collision etc....

Hello there, can I get some help with (b) please? first of all I wanted to ask.. can is it permitted to use different systems in one exercises? like f.e. for conservation of energy to find the velocity of ##m_3## I used as system only ##m_3## but for the collision I used the 3 masses as the...
31. ### Are Individual Normals Irrelevant in Solving a Pulley and Wedge System?

Is my answer correct? And if not, why?

33. ### B Displacement of Hanging Mass - Simple Pulley System

I'm having some kind of mental block. If I extend ##l_x## by ##\delta## ,I expect the hanging mass to move ##\frac{ \delta}{2}##. I can't figure out how this is the case from the constraint: $$l_x+l_1=C$$ ##C## is an arbitrary length I keep getting that ##l_1## changes by ##\delta##, but...
34. ### Acceleration of system related to rolling motion and pulley

There is no friction mentioned by the question so I assume the plane is frictionless but can the sphere roll without slipping if there is no friction? This is my attempt: Equation of translation motion of object A (assuming A moves upwards): TA - WA sin θ = mA . aCOM (A) TA = mA . aCOM (A) + WA...
35. ### A spring, disk and pulley system

(a) By setting up a coordinate system with the x-axis pointing to the right and the y-axis pointing downward we have ##\begin{cases}-kx_{eq}+T_1+F_{s}=0\\ -RF_{s}+rT_1=0\\ r_p (T_2-T_1)=0\\ -T_2+mg=0\end{cases}\Rightarrow x_{eq}=\frac{mg}{k}\left(1+\frac{r}{R}\right)## which coincides with the...
36. ### I Translational force of a pulley

Below is a pulley with mass and a string around it where the tension of one end of the string is 20 N and the tension of the other end of the string is 60 N. I know there is a net torque due to the differing tensions of the string, so I am wondering what the translational forces are on the...
37. ### Double pulley problem using Lagrangian

Setting up coordinates for the problem ##L=\frac{1}{2}M_1 \dot{x}^2+\frac{1}{2}M_2(\dot y-\dot x)^2+M_1gx+M_2g(l_a-x+y)## After using Euler Lagrange for x component and y component separate and substitute one to another then I get that ##\ddot{x}=\frac{M_1-2M_2}{M_1}g## whereas on the...
38. ### Buckets on a pulley - Dynamics Problem

A) I am not sure if initial velocity means the initial velocity of the putty. If then, it should be 10m/s. But the answer given is 10/7 m/s B) i have solved this part correctly C) the answer should be 86J Please be kind to help me
39. ### Olympiad dynamics problem with 3 masses and a pulley

Hello all, this is an adaptation of a question i saw some time ago (can't find the original now). There are two forces acting on two masses both 1kg. The masses are joined by an inextendable rope and going over a frictionless pulley of negigible mass. In blue I have written in some working out...
40. ### Work done by cord on the pulley

torque = rF = I*aT/r F = 0.5*aT*m_p W = F (tension in rope)*d = 0.5*aT*m_p*d Don't know because of unknown d
41. ### Euler-Lagrange equation: pulley system

##m_{A} = 3 kg## ##m_{B} = 2 kg## ##y_{A} + y_{B} = c \Leftrightarrow y_{A} = c - y_{B}##, where c is a constant. ##\Rightarrow \dot{y_{A}} = -\dot{y_{B}}## The Lagrangian: $$L = T - V$$ ##T =\frac{1}{2}m_{A}\dot{y_{B}}^{2} + \frac{1}{2}m_{B}\dot{y_{B}}^{2}## ##V = m_{A}g(c - y_{B}) +...
42. ### Leg suspended in a traction system

A leg is suspended in a traction system, as shown in the attached image. (a) Which pulley in the figure is used to calculate the force exerted on the foot? (b) What is the tension in the rope? Here T is the tension, wleg is the weight of the leg, and w is the weight of the load that provides the...
43. ### I Why doesn't the released mass m2 on pulley have higher acceleration?

Consider the pulley in the attached image to be frictionless. (a) If m2 is released, what will its acceleration be? My question is why wouldn't m2's acceleration be greater if released rather than attached to the string because m2 released is no longer subject to the string's upward force tension?
44. ### Pulley system to balance the weight of a person

Since we are dealing with an ideal rope, we have that ##T_1=T_2=T_3=F and T_2+T_3=2F=(m+m_p)g\Leftrightarrow F=\frac{m+m_p}{2}g.## ##T_4=3F+(m+m_p+M_p)g=\frac{3}{2}(m+m_p)g+(m+m_p+M_p)g=(\frac{5}{2}m+\frac{5}{2}m_p+M_p)g## and ##T_5=mg-2F.## Is this correct? If not, I woould appreciate a brief...
45. ### Pulley and weights hanging from spring balance

Net force acting downwards is ##5g-g=4g## in downward direction. Net force on pulley is ##2T-4g##. Weight measured by balance?
46. ### Three weights and two pulley problem

##Net force=50-T2+T2-T1+T1-20=10a## ##a=3 m/s^2## I want to ask when we do this way rather than taking individual masses we can’t decide the direction of the system as we can when they are taken individually. So is it correct to just leave ##a## as it is and solve ?
47. ### Analyzing a constraint eqn for a pulley system

I am having trouble creating the constraint equation for this pulley system. I don't understand why the last 3 variables of the following constraint is divided by 2? Could anyone help me understand why this is?
48. ### Inclined plane with pulley and spring

1) By the Work-Energy Theorem, ##W=K_f-K_i=\frac{1}{2}I_{0}\omega^2=\frac{L^2}{2I_0}.## 2) By assuming that the initial length of the spring is ##0##, calling its final length ##S## and ##T## the tension in the rope connecting the pulley and mass ##m_p## I have: ##\begin{cases}(kS-T)r=0\\ m_p...
49. ### Two Blocks, a Pulley and an Inclined Plane

1. ##-f_k\cos\theta-T\cos\theta+F_n\cos\alpha=m_2a_x## 2. ##f_k\sin\theta+T\sin\theta+F_n\sin\alpha-m_2g=-m_2a_y## 3. ##T-m_1g=m_1a_y## I am unable to get anywhere. There are accelerations in x , y directions. I need the value of acceleration. Then I can simply use ##s=ut+\frac12at^2##
50. ### Double Differentiation and Acceleration in a Four Pulley System

We can differentiate twice the y displacement with respect to time t and get the acceleration of block B. $$a_B= \frac12 m/s^2$$. But I don’t think it’s that simple.