Solving 3 Mass Pulley System: Acceleration & Tension Values

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In summary, the conversation is discussing a pulley system with three equal masses (m1=m2=m3=m). The question is to find the acceleration of the system and the values of the tensions T1 and T2. The first person is unsure about their calculations, but has determined the acceleration to be 1/3*g (3.33ms^-2). They are struggling with finding the values of the tensions T1 and T2 without knowing the mass. The final question is which equation to use to solve for the tensions.
  • #1
jamesbob
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Three equal masses (m1=m2=m3=m)are hung over a pulley as shown*. Find the acceleration of the system and the values of the
tensions T1 and T2?
I got the tension to be 1/3*g (=3.33ms^-2) this is probably wrong, but I am more stuck on the acceleration. Any help would be much appreciated.

*shown is: a pulley system with two masses on the left side and one mass on the right. all masses are equal. T1 is the tension above the upper mass (m2) on the left side. T2 is the tension between the 2 masses on the left side (m1 and m2).
 
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  • #2
Assuming I am visualizing this correctly, two masses on the left falling down with gravity, and by virtue of the cable, they are pulling the mass on the right up, which is all subject to the pull of gravity.

Acceleration = F/m

In a static system, T2=mg, since the line between m1 and m2 would suspend the lower weight, m1. However, since the masses are accelerating, T2 < mg.

T1 > mg, since gravity is pulling on m3 and accelerating m3 at the same time.

Remember Tension is just a force.
 
  • #3
Firstly thanks for your help so far. Sorry iv made a mistake in my first message. I got the Acceleration to be 3.3ms^-2 and I am stuck on the tension. Does that value for acceleration sound correct? I got it from doing:
a= (m1-m2)/(m1+m2)*g where in this case m1 is actually m1+m2 and m2 is m3.
m1=2m2 so m1-m2=2m2-m2=m2 and m1+m2=2m2+m2=3m2
so a = m2/3m2*g = 1/3*g = 3.33ms^-2 (taking g as 10ms^-2)
How can i get 'values' for the tension if i have no value for the mass? I'm guessing it will come from an equation where the masses cancel, but which equation? I know T=Ma or T-mg=-ma, any of them work?
 

1. How do I determine the acceleration and tension values in a 3-mass pulley system?

To determine the acceleration and tension values in a 3-mass pulley system, you will need to use Newton's laws of motion and the principles of equilibrium. First, draw a free body diagram for each mass, taking into account the forces acting on each one, including gravity, tension, and friction. Then, use the equations of motion to set up a system of equations and solve for the unknown variables.

2. What is the relationship between the masses and the acceleration in a 3-mass pulley system?

In a 3-mass pulley system, the acceleration will be the same for all three masses, regardless of their individual masses. This is because the masses are connected by a system of ropes and pulleys, which distribute the forces and result in a uniform acceleration for the entire system.

3. How do I account for friction in a 3-mass pulley system?

Friction can be accounted for in a 3-mass pulley system by including it as a force in the free body diagram for each mass. The direction of the friction force will depend on the direction of motion of the mass, and its magnitude can be determined using the coefficient of friction and the normal force.

4. Can the tension in the ropes ever be greater than the weight of the masses?

Yes, the tension in the ropes can be greater than the weight of the masses in a 3-mass pulley system. This is because the tension in the ropes is dependent on the acceleration of the system, which can be greater than the gravitational acceleration due to the pulley system.

5. What are the limitations of using equations to solve a 3-mass pulley system?

One limitation of using equations to solve a 3-mass pulley system is that it assumes ideal conditions, such as massless and frictionless pulleys and perfectly rigid ropes. In reality, these conditions may not hold true and can affect the accuracy of the calculated values. Additionally, the system may become more complex with multiple pulleys and additional forces, making it more challenging to determine a solution using equations alone.

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