Atwood machine pully problem with a twist

In summary, the conversation discusses how to find the tension in a cord holding up a simple pulley system with two masses, assuming the pulley is ideal and has no mass. The solution involves finding the tension in the rope holding the masses and using the fact that the total force on the pulley is 0 to find the tension in the cord. The conversation also briefly mentions that if the pulley does have mass, the moment of inertia must be taken into account. After some calculations, the final values for the tensions and acceleration of the blocks are determined.
  • #1
DukeJP2010
7
0

Homework Statement


A simple pulley has two masses on either end, one M1 and one M2. It is easy to find the acceleration of the two masses, and the tension on the rope suspending these masses. The pulley is suspended by a cord, however, and the question asks to find the tension in this cord that is holding up the pulley system.

Homework Equations


F=ma
Fnet=F1+F2+...

The Attempt at a Solution


I want to solve this one myself, but I need a pointer in the right direction.
 
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  • #2
Do a freebody diagram of the pulley. From what you've described the acceleration of the pulley is 0.
 
  • #3
so, would the tension of the cord holding up the pulley be twice the tension of the rope holding the masses?
 
  • #4
things to consider:
what is the mass of the pulley? what is the mass of the system (minus the cord), if it is an non-ideal pulley shall need to take into account moment of inertia.

in the simplest case of massless pulley, massless, non-stretchable string... what do you think is the answer? remember, tension must balance the force that trying to pull the pulley system down.
 
  • #5
DukeJP2010 said:
so, would the tension of the cord holding up the pulley be twice the tension of the rope holding the masses?

If it is an ideal pulley yes. As mjsd mentioned if the pulley has mass, then we need to consider the moment of inertia of the pulley...

I'm guessing "simple" pulley means ideal pulley. Plus they haven't given any information about the pulley, so we can assume it's ideal.
 
  • #6
Sorry for not stating that it is a massless, frictionless pulley and cord. The only things with mass are the two blocks. I omitted their numbers so i can get a point in the right direction.

There is a cord holding the pulley up (Tc) and then the tension of the rope (Tr) doing down, but twice (one for each mass) so this would yield:

0=Tc-2Tr

If that is correct I think i can solve the problem since i have already found the tension in the rope (Tr) using atwood machine equations.
 
  • #7
yup. looks right to me.
 
  • #8
After some quick work, can someone check this for me?

M1 = 1.2kg
M2 = 3.2kg

doing some math (that would be painful to type) yields:

a = 4.45 m/s2 (a = acceleration of the blocks)
Tr = 17.1 N
Tc = 34.2

Thank you all for your help.
 
  • #9
looks right to me.
 
  • #10
Once again, that you for your help.

Topic closed.
 

1. What is an Atwood machine pulley problem with a twist?

An Atwood machine pulley problem with a twist is a physics problem that involves a pulley and two masses connected by a string. The twist comes in when the pulley is not fixed and can rotate, causing the string to wrap around it. This adds a new element to the problem and changes the dynamics of the system.

2. How is the Atwood machine pulley problem with a twist different from a regular Atwood machine problem?

In a regular Atwood machine problem, the pulley is fixed and does not rotate, so the string remains straight. In the twisted version, the pulley can rotate, causing the string to wrap around it. This changes the distance and acceleration of the masses, making it a more complex problem to solve.

3. What are the key concepts involved in solving an Atwood machine pulley problem with a twist?

The key concepts involved in solving this problem are Newton's laws of motion, conservation of energy, and rotational dynamics. Newton's second law allows us to calculate the acceleration of the masses, while conservation of energy helps us determine the final velocities. Rotational dynamics is used to analyze the rotation of the pulley and the tension in the string.

4. How do you approach solving an Atwood machine pulley problem with a twist?

The first step is to draw a free-body diagram of the system, including all the forces acting on each mass and the pulley. Then, use Newton's second law and conservation of energy to set up equations and solve for the unknown variables. Finally, use rotational dynamics to determine the tension in the string and the rotational acceleration of the pulley.

5. What are some real-life applications of the Atwood machine pulley problem with a twist?

The Atwood machine pulley problem with a twist can be seen in many real-life situations, such as elevators, cranes, and exercise machines. It is also used in the design of mechanical systems, such as bicycle gears and transmission systems in cars. Understanding this problem can help engineers and designers create more efficient and effective systems.

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