Equilibrium Pulley Tension Problem

[livewire852]

Hello! I've been trying to understand this one for a while now, and think there might be a general mental block with regards to pulleys, tension etc.

Homework Statement

http://s3.photobucket.com/albums/y5...tions/?action=view&current=pulleyquestion.jpg
Question: "The system is in equilibrium and the pulleys are weightless and frictionless. The acceleration of gravity is 9.8 m/s^2. Find the tension T. Answer in units of N."

Homework Equations

w=mg?
Not really sure about these

The Attempt at a Solution

Right, so so far I've tried solving for T2 and T3 separately then solving the big T. Since the pulley on the right has only the 14N mass acting on it, then T2 should be 14N/2, or 7N right? Then for the second pulley on the left, I got
T3 + T2 - 19 = 0, which would make T3 = 12. Presumably this would make T = 24 N, but this isn't correct!
I imagine I am making some heinous oversight or massive assumption. Thanks in advance!

 

[PhanthomJay]

Hello! I've been trying to understand this one for a while now, and think there might be a general mental block with regards to pulleys, tension etc.

Homework Statement

http://s3.photobucket.com/albums/y5...tions/?action=view&current=pulleyquestion.jpg
Question: "The system is in equilibrium and the pulleys are weightless and frictionless. The acceleration of gravity is 9.8 m/s^2. Find the tension T. Answer in units of N."

Homework Equations

w=mg?
Not really sure about these

The Attempt at a Solution

Right, so so far I've tried solving for T2 and T3 separately then solving the big T. Since the pulley on the right has only the 14N mass acting on it, then T2 should be 14N/2, or 7N right?

right!

Then for the second pulley on the left, I got
T3 + T2 - 19 = 0, which would make T3 = 12. Presumably this would make T = 24 N, but this isn't correct!

Tension forces always pull away from the objects on which they act. Correct your error in signage.

 

[thomate1]

Hello! It seems like you are on the right track with your attempt at solving this problem. However, there are a few things you may want to consider in order to arrive at the correct solution.

First, it is important to remember that in a system in equilibrium, the net force and net torque must both equal zero. This means that the sum of all the forces acting on the system must be balanced. In this case, you have correctly identified that the tension T2 in the right pulley is 7N. However, you also need to take into account the weight of the 14N mass and the tension T1 in the left pulley. This means that the equation for the sum of forces in the vertical direction should be:

T1 + T2 - 14 = 0

Solving for T1, we get T1 = 7N. This means that the tension in the left pulley is also 7N.

Next, you need to consider the forces acting on the 19N mass. This mass is being pulled down by the tension T3, but it is also being pulled up by the tension T1. This means that the equation for the sum of forces in the vertical direction for this mass should be:

T3 - T1 - 19 = 0

Solving for T3, we get T3 = 26N.

Finally, in order to find the tension T in the rope, we need to consider the forces acting on the pulley itself. The tension T1 is pulling up on the pulley, while the tensions T2 and T3 are pulling down on the pulley. This means that the equation for the sum of forces in the vertical direction for the pulley should be:

T - T1 - T2 - T3 = 0

Substituting in our values for T1, T2, and T3, we get:

T - 7 - 7 - 26 = 0

Solving for T, we get T = 40N.

In conclusion, the tension T in the rope is 40N. It is important to carefully consider all the forces acting on the system in order to arrive at the correct solution. I hope this helps!