What is Atwood machine: Definition and 161 Discussions

The Atwood machine (or Atwood's machine) was invented in 1784 by the English mathematician George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics.
The ideal Atwood machine consists of two objects of mass m1 and m2, connected by an inextensible massless string over an ideal massless pulley.Both masses experience uniform acceleration. When m1 = m2, the machine is in neutral equilibrium regardless of the position of the weights.

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  1. Venturi365

    Solving for Masses in an Atwood Machine

    I've tried to solve this exercise but I haven't used one of the properties of the system (the displacement of the masses) so I don't know if I'm wrong about my procedure. First of all, we (obviously) know that $$ P=P $$ And since we can express the power of a force in two different ways, we...
  2. E

    System of Masses - Atwood Machine

    Would anyone verify whether or not I've formulated the proper Lagrangian here for the system above (the pulleys are massless, inextensible ropes of length ##L## and ##S##): $$\mathcal{L} = T - U $$ $$ \mathcal{L} = \frac{1}{2} m_1 { \dot l_1 }^2+ \frac{1}{2} m_2 \left( { \dot l_2}- {\dot l_1 }...
  3. rudransh verma

    Potential energy in case of Atwood machine

    ##T-2mg=2ma_1## (acceleration of heavier mass) ##T-mg=ma_2## (##-a_1=a_2##) On solving the eqns, ##a_1=-g/3=-a_2## ##s=1/2at^2## ##s=-g/6## , distance covered by heavier mass. ##s=g/6## , covered by lighter mass. Edit: ##\Delta U_1=mgh=-2mg^2/6## (decrease in U of heavier mass) ##\Delta...
  4. rudransh verma

    B Atwood machine -- Question about the pulley and weights

    I want to ask in this machine when there are two masses hanging down then the tension T is directed upwards along the rope. Is it the force applied by the rope on the mass? Is it the force applied by the pulley? When the anyone mass of the machine moves downwards is it because the force of...
  5. Istiak

    Find the equation of motion using the Lagrangian for this Atwood machine

    My understanding of the system from the image (which was given in book) I could see there's 3 tension in 2 body. Even I had seen 2 tension in a body. It was little bit confusing to me. I could find tension in Lagrangian from right side. But left side was confusing to me...
  6. A

    Dynamics of a double atwood machine

    I think the equations should be 𝑇−𝑚2𝑔=𝑚2𝑎1 𝑚3𝑔−𝑇=𝑚3𝑎1 𝑇1−𝑚1𝑔=𝑚1𝑎2 2𝑇−𝑇1=(𝑚2+𝑚3)𝑎2 P.S.- My textbook assumes T1 = 2T. I don't understand why that is so.
  7. V

    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...
  8. guyvsdcsniper

    What are the units for the slope in an Acceleration vs Mass Graph?

    I am doing an Atwood Simulation lab. I am having trouble with this part of my lab that ask the question provided. I can tell that the relationship is linear and that as the mass increases at a constant rate the acceleration increases. Logger pro tells me that the slope is 31.43. I am having...
  9. D

    Atwood machine calculation for launching a pebble

    Assume m2>m1 and take positive direction as downwards. String is inextensible so acceleration of block up = acceleration of block +pebble down =a I used the following 2 equations to obtain a ; -m1a = m1g - T , (m2+m)a = (m+m2)g - T which gives a = g(m+m2-m1)/(m+m1+m2) I then...
  10. B

    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...
  11. Asterast

    Question: Solving for Accelerations in an Atwood Machine System

    Summary:: I have solved the question but I'm getting answers wrong, some reaction equations seems to have trouble. Question: Let m1 = 1 kg, m2 = 2 kg and m3 = 3 kg in figure. Find the accelerations of m1, m2 and m3. The string from the upper pulley to m1 is 20 cm when the system is released...
  12. E

    Small error in calculating the value of g with an Atwood machine

    Hello, I hope you are very well ! I have a physics practical test where I have to find the gravitational acceleration with the Atwood machine: I've found 9.27 m/s² and have to say what could have caused this slight gap. They say that there is no friction in this experiment. I can't really...
  13. P

    Why is tension (T) only added to one side of an Atwood Machine?

    I solved for a1 prior to the force (f) being added. -a1 = a2 and T = m1*a1 + m1*g T = m2*a2 + m2*g <--substitute -a1 = a2, multiply everything by -1, add the two equations in order to solve for a1 (and thus also a2) T = m1*a1 + m1*g -T = m2*a1 - m2*g 0 = m1*a1 + m1*g + m2*a1 - m2*g...
  14. L

    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...
  15. UnPetitGarcon

    The acceleration of a massless pulley in a double Atwood machine

    So there is a textbook physics question in which it asks us to calculate the acceleration of pulley B(which is massless). This exact question was posted and asked previously in this thread. However, it didn't discuss my doubt. To be exact, the question I have troubles with is (b)...
  16. solarcat

    Atwood Machine Massive Pulley

    A net torque is required to make the pull rotate, so this can only occur if the tension forces differ. I know mass 1 will accelerate upwards and mass 2 will accelerate downwards, so T1>mAg and T2<mBg. But I don't know where to go from there.
  17. Abhishek11235

    Troubleshooting a Discrepancy in Atwood Cylinder Solution

    Homework Statement The problem is in attached screenshot. Now,I solved this using force/torque method. However ,I got different solution as given in solution manual. Where I have gone wrong? Homework EquationsThe Attempt at a Solution Applying F=ma to cylinder: $$mg-T=ma$$ Applying ##\tau =...
  18. O

    How Does the Speed of Block B Compare in a Three Mass Atwood Machine?

    In the cable-pulley system shown here, block A is moving upwards at a speed of 5m/s and block C is moving downwards at a speed of 2.5m/s. What is the speed of block B? (See attached picture) This seems easy, I just want to make sure I'm not crazy. If mass B moves downward some distance d...
  19. T

    Atwood machine with variable mass

    Homework Statement We have an Atwood machine like the picture below. one side (left) is a bucket full of water which has a hole on the bottom and the water is flowing with rate ##dm/dt = \alpha = const##. The initial mass of bucket with the water is ##m_0##. On the other side (right) we have a...
  20. arturo

    Half Atwood machine: acceleration after inital force

    Homework Statement Assume that the block on the table (Figure 1) has twice the inertia of the hanging block. (a)You give the block on the table a push to the right so that it starts to move. If the magnitude of the frictional force exerted by the table on the block is half the magnitude of...
  21. J

    Is the block moving in an Atwood machine when climbing up a rope?

    Homework Statement [/B] As stated in the included pics, you are climbing up a massless rope on a frictionless pulley, attached to a block equal to your mass which is hanging on the other side. You move a distance d along the rope. Does the block move? If so, how much? Homework Equations F =...
  22. john-b

    Potential Acceleration of an Atwood Machine

    Homework Statement In the diagram, m1 has a mass of 47 kg and m2 has a mass of 35 kg. The coefficients of friction between m1 and the surface of the inclined plane are µs = 0.42 and µk = 0.19. (a) If the masses are held in place and then released, will they start to move? (b) If the answer...
  23. I

    Calculating Accelerations in an Atwood Machine with an Applied Force

    Homework Statement The masses of blocks ##A## and ##B## are 20kg and 10 kg, respectively. The blocks are initially at rest on the floor and are connected by a massless and frictionless pulley. An upward force ##\vec{F}## is applied to the pulley. Find the accelerations ## \vec{a_A}## of block...
  24. D

    Kinetic energy of a compound system (atwood machine)

    A system is defined as two connected masses in an atwood machine and the earth. How do I find total kinetic energy in a system where more than one object is moving (or is only one object actually moving since the two masses are connected with a string? idk) This is an isolated system so... ΔK...
  25. D

    Finding the decrease in potential energy of atwood machine

    Homework Statement In the system below, m1<m2. When the object of mass m2 has descended a distance h, the potential energy of the system has decreased by: Homework Equations the answer is (m2-m1)gh The Attempt at a Solution I used ΔU= Uf-Ui m1gh-m2gh=ΔU (I think that the decrease in...
  26. L

    "Shifting" non-inertial frame in Accelerating Atwood Machine

    Hello, I was referring to this thread: https://www.physicsforums.com/threads/accelerating-atwoods-machine-problem.44305/ to solve a problem on accelerating atwood machines in which, naturally, one attempts to find the acceleration of each of the individual masses. Although I now understand how...
  27. A

    Effects of Rolling Resistance on Tension and Acceleration in an Atwood Machine

    We had a lab using an Atwood Machine with block A being on the surface and block B as the hanging object with different masses each round. Rolling resistance was present. Question 1 asked whether or not the tension in the string was less than, greater than or equal to the magnitude of the...
  28. dsfrankl

    Double Atwood Machine Problem

    Homework Statement If the masses for a double Atwood machine similar to the own shown in the attached picture are m1=2.0kg, m2=3.0kg, and m3=8.0kg: (a) what is the magnitude of the acceleration of the system and (b) how would you draw free-body diagrams for this problem? NOTE: m3 does not...
  29. L = K - U

    Infinite Atwood Machine (Morin Problem 3.3)

    I could've peeked at the solution manual and end with it at that. However, I'm trying to change this nasty habit and solve this problem myself. I might be too ambitious. Here goes. Homework Statement Consider the infinite Atwood's machine shown. A string passes over each pulley, with one end...
  30. I

    What is the acceleration of the masses in a double double Atwood machine?

    Homework Statement This is actually a problem I solved but I'm having trouble reconcile the answer with my intuition (Check the end of the post for my actual question). The problem: Find the acceleration of the masses for the double double Atwood machine (see figure) The masses are from left...
  31. Vitani11

    Velocity of masses on an atwood machine?

    Homework Statement 2 masses m1 and m2 are attached by a string to a massless pulley. mass 1 is on the surface while mass 2 is hanging off. mass 1 experiences a friction force (mu)k. What is the acceleration of the system? What is the velocity of mass 1 in terms of mass 2? Homework Equations...
  32. R

    Atwood Machine: Find M in Terms of m1 & m2

    Homework Statement In the Atwood’s machine, what should M be, in terms of m1 and m2, so that it doesn’t move? Homework Equations F=ma The Attempt at a Solution I've set T1=Mg as T1 is the tension of the rope attached to M. m1 and m2 are both connected together by the same rope so I assumed...
  33. Turkus2

    Effective Friction Related to Pulley Radius (Atwood Machine)

    First time posting on the forum - I've been coming here a lot the past year or so to seek answers. This one is concerning a lab. I think I've already done the legwork but am sort of looking for either something I'm missing or a confirmation of sorts. It's pretty messy and wordsy but if you...
  34. B

    I Intuitive Explanation of an Atwood Machine

    So I'm working through a physics a textbook on my own, and because of that don't always have a professor who can help explain concepts I don't understand, so I'm turning to you good folks. Could someone explain why both masses need to be taken into account when determining the acceleration of...
  35. L

    Atwood's machine with two connected discs

    Homework Statement The system looks like this: I have two discs which are connected. Disc 1 has ##R_1##(radius) and ##M_1##(mass) Disc 2 has ##R_2## and ##M_2## ## R_2 > R_1 ## ## M_2 > M_1 ## on both discs weights are attached on opposite sides. On smaller ##m_1## is pulling and on bigger...
  36. C

    Understanding the Motion of Double Pulleys: Exploring Acceleration and Forces

    Homework Statement A mass m1 is hung on a pulley with another pulley on th eother side with two masses;m2 and m3.Find the accelerations of the masses Homework Equations F=M.a a1=-(a2+a3)/2 The Attempt at a Solution So in my book ,the solution provided was 2T-m1g=m1a1 T-m2g=m2a2 and T-m3g...
  37. D

    Coefficient of Friction of Fixed Atwood Pulley

    Homework Statement Hi, I was wondering how you would isolate for and calculate the coefficient of friction in an Atwood pulley, with one fixed pulley, with two masses hanging off of it on either side. There is no table or surface that the masses are touching or resting on, they are both...
  38. defaultusername

    Is the Tension Force in an Atwood Machine Only Transmitted Between Blocks?

    Homework Statement When talking about an Atwood machine, a student states: Is the student correct or incorrect? Why? Homework Equations Tension = mg + ma The Attempt at a Solution This is how it is making sense in my mind, but correct me if I'm wrong. I am thinking that the student is...
  39. S

    Double pulley Atwood machine (with 3 masses)

    Homework Statement I need help with number 4. Also I am altogether unsure of this problem... if you catch any mistakes, point them out! :) Homework Equations F = ma Here are the variables I used in my attempt at the solution mx = m subscript 1, 2, or 3 ±a1 = acceleration of either mass on...
  40. firefox

    Negative Moment of Inertia from Atwood Machine Experiment?

    I'm currently completing an Atwood Machine Experiment with two 100g weights on either side of the pulley, with a variance in weight created by attaching dimes and pennies to either side of the weights. The point of the experiment is to validate: (m1 – m2)g = (m1 + m2 + I/R2) Homework Statement...
  41. K

    Atwood Machine, finding mass

    Homework Statement atwood machine: pulley with negligible mass and frictionless with 2 blocks hanging at rest. The first block "m" has a mass of 3.66kg The second Block "M" is unknown The blocks are released; block M accelerates at .255*g m/s2 downward Find the mass of block "M" Hint: There...
  42. J

    Atwood Machine Lab Homework: Solve for Moment of Inertia

    Homework Statement I am given the equation (m1 – m2)g = (m1 + m2 + I/R2)a and the experiment is to validate this equation. Homework Equations The Attempt at a Solution After following the lab guide, it tells you to plot the weight difference (m1– m2)g against acceleration and determine...
  43. S

    Tension force in Atwood machine

    I've read a couple other threads about this issue. And one even addressed my exact question but the answer didn't help me understand this at all. In an Atwood machine, why isn't the total force on a mass = its gravity minus the gravity of the mass on the other side? I keep seeing tension in...
  44. R

    Atwood Machine Inertia Friction and directional forces

    I have an Atwood Machine. I have an aluminium Pulley of radius 4 inch. A gym cable running over it. Not sure coefficient of friction but smooth movement. One end of rope, I attach wt. of 0.5 kg. I had to attach weight of 1 kg for acceleration to start. If I attach 2 kg, I had to attach 3.1 kg...
  45. I

    How to find mass in an Atwood machine

    Homework Statement A pumpkin and a weight are attached to a frictionless pulley. As the 5kg weight is released, the pumpkin accelerates down at 4.65 m/s^2 to the ground. What is the mass of the pumpkin? [/B]Homework Equations How do I find the mass? The Attempt at a Solution T=m1g ma=m2g-T...
  46. K

    Half atwood machine with accelerating pulley

    Homework Statement [/B] Consider a half-atwood machine on a cart as below, with mass m_2 attached to M via a frictionless track that keeps it pinned to M but allows it to move vertically. All surfaces (except between the wheels/ground) are frictionless, and the pulley and rope are massless. If...
  47. B

    The double Atwood machine has frictionless, massless pulleys

    Homework Statement The double Atwood machine has frictionless, massless pulleys and cords. Determine (a) the acceleration of masses ma, mb, and mc, and (b) the tensions Fta and Ftc in the cords. Homework Equations F=ma The Attempt at a Solution So I drew free body diagrams for the mass A...
  48. M

    Atwood Machine, deriving equation for acceleration

    Homework Statement I still don't got the hang on Atwood Machines, and i don't know if I am wrong here or just overthinking it. But i got this one exercise where i am kind of stuck in two of the sub-exercises. So I am hoping there is someone here who could guide me in the right direction.Atwood...
  49. Rations

    Faulty approach to solving a double Atwood's machine

    Hello. I'm wondering why my approach to solving this problem (Morin 3.2) is faulty. Homework Statement A double Atwood's machine is shown, with masses ##m_1##, ##m_2##, and ##m_3##. Find the accelerations of the masses. Homework Equations ##F = ma## The Attempt at a Solution Let's say the...
  50. bananabandana

    Does Acceleration Affect the Stability of an Atwood Machine in an Elevator?

    Homework Statement Please see attached for diagram. We know that the elevator arm is horizontal when the lift is stationary, with ## M_{1}=\frac{4M_{2}M_{3}}{(M_{2}+M_{3})}## It wants us to find out if this is still the case when the lift is accelerated upwards at a constant velocity ##g##...
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