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.
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...
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 }...
##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...
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...
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...
I think the equations should be
๐โ๐2๐=๐2๐1
๐3๐โ๐=๐3๐1
๐1โ๐1๐=๐1๐2
2๐โ๐1=(๐2+๐3)๐2
P.S.- My textbook assumes T1 = 2T.
I don't understand why that is so.
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...
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...
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...
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...
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...
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/sยฒ 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...
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...
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...
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)...
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.
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 =...
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...
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...
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...
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 =...
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 ยตs = 0.42 and ยตk = 0.19.
(a) If the masses are held in place and then released, will they start to move?
(b) If the answer...
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...
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... ฮK...
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 ฮU= Uf-Ui
m1gh-m2gh=ฮU (I think that the decrease in...
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...
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...
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...
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...
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...
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...
Homework Statement
In the Atwoodโs machine, what should M be, in terms of m1 and m2, so that it doesnโt 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...
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...
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...
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...
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...
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...
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...
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
ยฑa1 = acceleration of either mass on...
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 โ m2)g = (m1 + m2 + I/R2)
Homework Statement...
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...
Homework Statement
I am given the equation (m1 โ 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 (m1โ m2)g against acceleration and determine...
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...
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...
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...
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...
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...
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...
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...
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##...