Pulley/Torque problem where pulley has mass

In summary: T_1 and m_2 will have a kinetic energy of m_2g-T_2. The work done in moving the blocks from their original position to the new position is m_2a-T_2.
  • #1
tron_2.0
29
0
hi, I am new to the forum =] my names suraj and I am an engineering/journalism student in my first year. this forum looked pretty informative so i figured id sign up. anyways id really appreciate it if someone could help me out on this problem.

Homework Statement



Consider two objects with connected by a light string that passes over a pulley having a moment of inertia of about its axis of rotation as shown in the figure below. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance .

(a) Use the principle of conservation of energy to find the translational speeds of the objects as they pass each other.
(b) Find the angular speed of the pulley at this time.


Homework Equations


well not given in the problem but i believe you have to apply:
-Free Body Diagrams (of both masses)
-Torque=Fd
-Kinematics

The Attempt at a Solution



okay well i tried to solve it in the variable form that the question is asking for, and i was unable to do so. however i tried to plug in some numbers (give each mass a numerical mass, give the pulley a random mass, etc) and i believe i solved the problem. I am just confused as to how i should solve it in the form using variables?


this is what i got when i made up values for the pulley's mass, the pulley's radius, the mass of the weight on the left, and the mass of the weight on the right:

http://i21.photobucket.com/albums/b277/riceboy89/solution1.jpg [Broken]

however it is asking me the answer in terms of variables, and I am having a hard time trying to find my acceleration in terms of variables so i can use the equation i ended up in the above solution (i figured that if i can solve for a in terms of variables, can't i just plug it into v=sqrt(2a*deltaY)?)

http://i21.photobucket.com/albums/b277/riceboy89/solution2.jpg [Broken]

thanks for the guidance
 
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  • #2
Hi Suraj!

In http://i21.photobucket.com/albums/b277/riceboy89/solution2.jpg" [Broken] pic, as

[tex]m_1>m_2[/tex] the equations should be

[tex]m_1g-T_1=m_1a[/tex]

and

[tex]
T_2-m_2g=m_2a[/tex]

The [tex]\tau=I\alpha[/tex] equation looks good to me.
 
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  • #3
You will have a loss in PE balanced by a gain in KE and work done.

What is it that loses PE, and by how much ?

What are the gains in KE and by how much ?

What work is done and how much ?
 
  • #4
google_spider:

am i on the right track in finding the acceleration first, in terms of variables, and then plugging it into the equation (sqrt(2a*deltaY))?
 
  • #5
tron_2.0 said:
am i on the right track in finding the acceleration first, in terms of variables, and then plugging it into the equation (sqrt(2a*deltaY))?

What is [tex]a_y=\sqrt{2a\delta y}[/tex] ?? I have never come across this formula. As Phisixguru pointed out, you have to use energy conservation. Both the blocks will be at a height of 4H when they pass each other.
 
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1. How does the mass of the pulley affect the torque in a pulley/torque problem?

The mass of the pulley does not affect the torque in a pulley/torque problem. Torque is determined by the applied force and the distance from the axis of rotation. The mass of the pulley only affects the overall acceleration and velocity of the pulley system, but not the torque.

2. Can a heavier pulley be used to increase the torque in a pulley system?

No, using a heavier pulley will not increase the torque in a pulley system. As mentioned before, torque is determined by the applied force and the distance from the axis of rotation. The mass of the pulley will not change these factors.

3. How do I calculate the torque in a pulley/torque problem where the pulley has mass?

The torque in a pulley/torque problem can be calculated by multiplying the applied force by the distance from the axis of rotation. If the pulley has mass, the torque can also be affected by the moment of inertia of the pulley, which is a measure of the pulley's resistance to rotation. This value can be calculated by using the mass and radius of the pulley and plugging it into the formula: I = 1/2 * m * r^2.

4. Is there a difference in torque between a massless pulley and a pulley with mass?

In theory, there is a difference in torque between a massless pulley and a pulley with mass. However, in most practical scenarios, the difference is negligible and can be ignored. This is because the mass of the pulley is usually much smaller compared to the other masses in the system, so its effect on torque is minimal.

5. What happens to the torque if the pulley's mass is not evenly distributed?

The torque will still be determined by the applied force and the distance from the axis of rotation, but the moment of inertia of the pulley will be affected. If the mass is not evenly distributed, the moment of inertia will be different and will need to be calculated accordingly. This could affect the overall acceleration and velocity of the pulley system, but the torque itself will not be directly affected.

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