# What is Pulley system: Definition and 352 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. ### Time period of SHM & Energy conservation in pulley-spring-block system

TL;DR Summary: I was solving this problem given in a book. The answer I got was wrong and seems to violate the conservation of mechanical energy. Yet the forces were balanced. Can someone provide an explanation. So here is the problem: In the above arrangement, I had to find the time period...
2. ### Scarf modelled as a pulley system / F=ma exercise

My teacher gave the above answer as a solution. However, I am not convinced that the proportion is really $$\frac{m_1}{m_1+m2}$$. If m2 << m1the proportion would be really big, right? But intuition tells me that it should be the opposite. Furthermore, if m2 >> m1, then one would expect the...
3. ### Newton's Second Law (Pulley Sustem)

Two masses, M1=4.0 Kg, and M2=20 Kg, are attached by a rope that crosses over a massless, frictionless pulley. M1 slides horizontally and experiences a kinetic frictional force due to its motion across the surface. The coefficient of kinetic friction is uk = 0.638. When solving the problem...
4. ### 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...
5. ### 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!
6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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}) +...
10. ### 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...
11. ### 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?
12. ### 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.
13. ### Tension in a pulley system pulled at an angle

This problem just came to my mind when thinking on another problem. Does the tension is just 2T as it is if the angle "a" is 90 degrees? It seems not to me. In a "normal"( I don't really know what is the right word for that) situation, the tension is would be 2T at the line in the middle of two...
14. ### Misc. Display built with a rotating cube design

Hello everyone, I want to build a rotating display cube (will be mounted on a wall, those cubes that has shops logos ect..), my problem is that I don't know where to start and how to attack the rotating mechanism. I have a 1400Rpm moteur (and it's a 1m per 1m cube that weights around 120kg-150kg...
15. ### 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!
16. ### 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...
17. ### Find the unknown mass on a inclined rope pulley system.

First I calculated the forces that were working against mass B. m(A)g sin 30 + μm(A)g cos 30 = 12.86 N The force working with mass B is m(B)g = 9.8m(B) I thought I could solve for B using F=ma where 12.86 N = (2kg+m(B))*(0.58), but of course, 12.86 N is just the force required to make the...
18. ### Finding the period of pulley system

This is not homework. I found this question when browsing and there is also solution but I do not understand it. This is part of the solution: My questions: 1) From equation (i): ΔT = m.a, I think ΔT refers to W - T (weight of block - tension of string). I got this from free body diagram and...
19. ### Pulley system for cardboard pulp shredder/mixer

Hi everybody, first message on this forum ! I am building a machine for a friend who works with cardboard pulp, he is also a performance artist and would like a machine where 2 or 3 performers can activate the machine by hand with pulleys and wheels, and shred the pieces of cardboard that are...
20. ### Pulley system -- Calculate the mass that balances this pulley system

I've been stuck at this pulley system for a while. I've calculated the force of which A pulls => FA = sin25*50*9.82 = 208.5 N But I get stuck on the free body diagram. Can someone help and explain the freebody diagram

22. ### Ideal Vs Real Mass Pulley system

Below is an ideal mass pulley system that we encounter in many problems under Newton's Second Law of Motion questions. Its supposed to be massless and frictionless i.e. string slips over the pulley and pulley does not rotate. In a real system, the pulley is assumed to be massless, whereas in...
23. ### Calculate pulley system loads

Hello, I'm working with a pully system and can't find the answer for this question on Google. I'm wondering how to calculate the load on the rope in order to determine what grade rope I should use. For example let's say I'm picking up a 100 lb box using a 4 to 1 system. Not accounting for...
24. ### Find the load saved by a pulley system

There are 3 different strings in this system. The one pulling P, the one pulling F and the one pulling a pulley. Since the questions says they're ferried across before hitting mast or deck, I'm assuming that they are not stationary. g is gravitational acceleration. P will move twice as fast...
25. ### 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...
26. ### 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?
27. ### Choosing proper coordinates in a complex 2 pulley system

FBD Block 1 FBD Block 2 FBD Pulley B I'm mainly concerned with the coordinate system direction in this problem, but just to show my attempt, here are the equations I got from the system. ##-T_A + m_1g = m_1a_1## ##T_B - m_2g = m_2a_2## ##T_A - 2T_B = 0## Using the fact that the lengths...
28. ### Pulley angular velocity problem

Further given: - every beam is infinite stiff - pulleys are massless - cables don't stretch, no slip, and frictionless. -Every pulley has a diameter D except pulley Q. Pulley Q has diameter 0.5*D So what I don't understand is how to calculate/determine the velocity at R and S. Can someone help...
29. ### Distance traveled and period of a mass - spring - pulley system

1. How will the motion of M be? I assume wire S is inelastic so will M move downwards but not in straight line? (I mean M moves downwards but because the left side of pulley is connected to S, it will be static and the right side of pulley can go down along the extension of the spring so its...
30. ### Mechanics Question- Massive Rope in a Pulley System

I understand how they might have got to these answers but I'm still kind of shaky on how the mass of the rope plays a role in the tension at point B, and how to mathematically represent the tension at any point along the rope; I know the tension varies because the rope has mass. If I was to...
31. ### D'Alembert's principle on a pulley system

This is the problem's picture: My problem is that what I got for one acceleration (m3's) via Newton's equations is not the same as via D'Alembert's principle (I've checked on my PC if they are the same expression). I can't find the mistake. Any suggestion is welcome. I attach pictures of what...
32. ### Virtual work in a pulley system

If 1kg make a displacement of 1unit upward then A make a 1/2unit down because 1/sin 30.after that i have no idea what do I will really need help. Thanks!
33. ### About the constraint equations of a pulley

See the solved example as shown in the image. I don't understand how can we write S(A)=2S(B) since integrating V(A)=2V(B) will give us an extra unknown constant and the work done by friction will depend on it. I found the relation 2S(B) + S(A) = const. (somebody confirm if this is right?) so...
34. ### Oscillating Spring in a Frictionless pulley system

1. Draw Free body Diagram for each weight. 2. Solve for Tension in Rope. 3. Find Spring Constant. 4. Find omega (w, or angular velocity)
35. ### How to change pulley direction?

Hello Guys, Maybe someone can be at my assistance in this one. I have a similar airer as on the attached picture and i would like to change a set up of pulleys and possibly to add some more of them, in a way that I do not want to pull it down by the side wall anymore. Instead, I would prefer...
36. ### Energy conservation for objects hanging from a pulley

I have some conceptual questions about this task. In order to get the correct result (I checked the textbook answer) in part (a) I had to assume that the speed for each block is the same at all instants. And that if one block moves down x meters, the other one will move up that same amount of...
37. ### Acceleration of masses in a pulley system

So I figured out the equation, but it is probably wrong because the answer doesn't tally. Since the string is inextensible, I can assume that tension is the same for both sides, and acceleration for both masses is the same too So: I can say that the acceleration of 2kg block =acceleration of 7kg...
38. ### Length of a string over a 2 pulley system

Hello all, I am working on a lab report for physics, and am a bit stuck on one aspect. The basic layout of the pulley system is attached. (This is a diagram I made, so if there are any inaccuracies in this one either, I am happy to fix it. So, I mostly understand the lab. My TA said, though...

40. ### Help with a pulley problem with 3 masses

The figure : What I understand from the figure : T1=m1a1 T2=m2a2 T3-m3g=m3(-a3) - The three masses given all have different mass so each of them has different acceleration - How do one substitute to obtain the answer for a3? - I've tried to substitute to find the value of a3, but it seems...
41. ### Finding the acceleration of a pulley system including an inclined plane

This question showed up on my grade 12 physics test. The problem I have with this question is that I did not know the direction that the system would accelerate in, so I just solved as though the mass on the inclined plane would accelerate the system. I expected that if it would accelerate the...
42. ### Conservation of energy: a mass and pulley system

The solution is an application of the law of conservation of energy. Start with equation (1). The masses are in equilibrium and are not accelerating. This implies that ΔK = 0, because the kinetic energy will not change without acceleration. Thus, we are left to find equation (2) in terms of θ...
43. ### Pulley system with relative motion

Well, first I tried to understand the relation between the velocities and accelerations of both bodies and I got that the velocity of ##B## is half the velocity of ##A##. This is because a change in length of the cord "that touches ##A##" must be equal to the change in length of the two cords...
44. ### Mechanical advantage of a pulley system

I don't know how the bottom two pulleys affect the top one. From what I know, the three ropes should have the same tension, the force of the body, divided between them. So if we take top one, it should have that tension on both sides, but also should support the other two pulleys below it. That...
45. ### Acceleration in a pulley system

SOLUTION ATTEMPT Newtons 2nd law states that F=ma (eq. 1). When a force is applied to a mass m it results in an acceleration a=F/m (eq. 2). If a vertical force is applied to one of the objects in this system, acceleration of both objects will occur. Assuming the length of the rope is constant...
46. ### Explain friction in a pulley system

Hi! I'm working in a new area and I'm looking for inputs/suggestions for relevant factors to look into and possible ressource where I can read about this :) I did some tests in a pulley similar to the one below. I had a fixed weight at M2. I started with M1=M2 but added weights to M1 until...
47. ### Pulley system, find the acceleration and tension

Homework Statement Given the picture: Make the free body diagrams of each body and the pulley. Remember that there are two different strings therefore there are two different tensions.Assuming that the mobile of mass M starts from rest and has a displacement D at a time t, and the bodywith...
48. ### (Mechanics) Pulley System Question

Homework Statement Derive an expression for the angle alpha and determine the initial horizontal and vertical forces exerted at the point of attachment of the bell rope to the plank. The system is in static equilibrium Both ropes are light ie negligible mass. The point of attachment has been...
49. ### Pulley System Part c: Homework Statement & Relevant Equation

Homework Statement 2. Relevant equationThe Attempt at a Solution ...[/B] Part c) I'm confused as to how the actual pulley system works. If its balanced wouldn't it be stationary. How does it move? I thought that since its balanced the acceleration of the system is constant and therefore to...
50. ### Finding the acceleration of two masses on a pulley system

Homework Statement Two blocks of the masses m1=7.40 kg and m2=m1/2 are connected via a massless pulley and massless string. The system is currently in equilibrium but is about to start sliding, if m2 would increase even by a bit. For the friction between the surface and m1 assume that µs=µk...