Physics Problem - [Dual Pulley]

In summary, the conversation is about a physics problem involving two 10.0 kg masses suspended from a dual pulley. The total mass of the pulley is also 10.0 kg and the question is to find the acceleration of mass m_{1} connected to the larger shaft. The conversation also includes a picture and equations to help solve the problem. One person gives a hint to think about the Moment of Inertia and another suggests using a constraint equation to solve the problem.
  • #1
Boltak
2
0
Hi everyone...

I've been struggling with a physics problem for 2 days now... I'm really not sure what to do.

Problem -
A pair of 10.0 kg masses are suspended from (massless) strings wrapped around a dual pulley. The radius of the smaller shaft on the pulley is half the radius of the larger shaft on the pulley. If the total mass of the pulley is also 10.0kg, and the pulley is considered to be a uniform disk, what is the acceleration (magnitude and direction) of mass ([tex]m_{1}[/tex]) connected to the larger shaft?

Basically... one 10.0 kg mass is attached on the right side of the small shaft, while other 10.0kg mass is attached to the left side of the bigger shaft.

picture at http://members.cox.net/lorddreg/p9.jpg

I was assuming [tex]m_{1}[/tex] would most likely accelerate down.

This is what I have so far... I'm not sure if it is correct or not ...

For [tex]m_{1}[/tex] ...
[tex]\sum{F = m * a_{y} = -T_{1} + m_{1} * g}[/tex]

For [tex]m_{2}[/tex] ...
[tex]\sum{F = m * a_{y} = T_{2} - m_{2} * g}[/tex]

I would appreciate any help!

Thank you
 
Last edited by a moderator:
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  • #2
This looks like a homework assignment, so I'll give you a hint. :smile:

Think about the Moment of Inertia of your system... :wink:

Good luck!
 
  • #3
You need a constraint equation to solve the problem i.e the relation between T1 and T2 the two pulleys have same angular acceleration which u can relate with two end of ropes just at the surface of the pulley.
 
  • #4
U got 2 equations, u need the third equation which is constraint equation
Remember
No. of Equations = No. of variables
 

1. What is a dual pulley system?

A dual pulley system is a mechanical system that consists of two pulleys or wheels with a belt or rope connecting them. The belt or rope wraps around both pulleys, creating a loop, and allows for the transfer of force and motion between the two pulleys.

2. How does a dual pulley system work?

A dual pulley system works by using the concept of mechanical advantage. The effort force applied to one side of the pulley is multiplied on the other side, allowing for a smaller force to lift a larger load. The direction of the force is also changed, making it easier to lift the load vertically.

3. What are the advantages of using a dual pulley system?

There are several advantages to using a dual pulley system, including increased mechanical advantage, reduced effort force, and smoother operation. It also allows for the transfer of force and motion over longer distances without losing efficiency.

4. How do you calculate the mechanical advantage of a dual pulley system?

The mechanical advantage of a dual pulley system can be calculated by dividing the load force by the effort force. For example, if the load force is 100N and the effort force is 50N, then the mechanical advantage would be 2.

5. What are some real-life applications of dual pulley systems?

Dual pulley systems are commonly used in elevators, cranes, and other lifting equipment. They are also used in exercise equipment, such as weight machines, and in industrial settings for moving heavy loads. Dual pulleys can also be found in simple machines, such as a clothesline or a flagpole.

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