2 pulley system with three masses. Find the two outside masses.

In summary, the conversation discusses a lab involving a 2 pulley system with three masses and a string in the shape of an "m." The known mass is .200 kg and the angles between the strings are given. The task is to find the unknown masses, and the conversation discusses using trigonometry and summing forces to solve for the tensions and ultimately the unknown masses.
  • #1
manderzz
2
0
Okay, so I did a lab where we had a 2 pulley system that involved a string and three masses. The string is set up so it is in the shape of an m when put on the pulleys. The known mass is put on the middle string (m3) hanging down and the two outside masses (m1) and (m2) are unknown and are not equal to each other. The middle mass is .200 kg. The angle between T1 and T2 is 80 deg the angle between T1 and T3 is 150 deg and the angle between T2 and T3 is 130 deg. I need to find M1 and M2. I drew a fbd and know that T1y and T2y must be equal to the magnitude of T3. Thank you in advance.



T1cosθ+T2cosθ+T3=0



I have been trying to work with my free body diagram to figure out the T1y and T2y values by using Pythagoras. I know that the middle mass has a weight of (9.8)(.200 kg)=1.96 N. So the T1y and T2y need to add up to equal this. I have no idea where to start, any help would be so appreciated!
 
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  • #2
Lets see if I have this right:

A string goes from m1, over a pulley, to m3; and another string goes from m3, over another pulley, to m2.
The whole situation is static - no motion.

Then sum the forces to zero.
m1 and m2 are hanging vertically - held by tensions T1 and T2 respectively.
Which gives you T1 and T2 right away - in terms of m1 and m2.

m3 is hanging from two angled strings, tensions T1 and T2 again - since the tension has to be the same over each pulley. I don't know how you get 3 tensions.

T1 acts upwards at angle A to the vertical and T2 acts unpwards at angle B to the vertical.
The remaining force is the weight - vertically downwards.

The horizontal and vertical components must sum to zero.
You need to use trigonometry to get the components of T1 and T2.
 
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  • #3
Yes, that is the set up. The strings are held together by a knot if that makes a difference, and I have drawn a fbd of the known forces on the knot. Thank you, I will try it again with the information you have given.
 

1. How does a 2 pulley system with three masses work?

A 2 pulley system with three masses consists of two fixed pulleys and three masses attached by a string. The string goes over both pulleys, with one end attached to the middle mass and the other end attached to an outside mass. When one outside mass is pulled, the other outside mass moves in the opposite direction due to the tension in the string. This creates a mechanical advantage, with the force exerted by the outside masses being greater than the force applied to the middle mass.

2. What is the purpose of a 2 pulley system with three masses?

The purpose of a 2 pulley system with three masses is to create a mechanical advantage, allowing for easier movement of heavy objects. The outside masses act as counterweights, balancing the force needed to lift the middle mass. This system is commonly used in mechanical engineering and physics experiments.

3. How do you calculate the force in a 2 pulley system with three masses?

The force in a 2 pulley system with three masses can be calculated using the formula F = (m1/m2) * T, where F is the force exerted by the outside masses, m1 is the mass of the middle mass, m2 is the mass of one outside mass, and T is the tension in the string. This formula assumes an ideal system with no friction or other external forces.

4. Can a 2 pulley system with three masses be used to lift any weight?

No, a 2 pulley system with three masses has a limited lifting capacity. The force exerted by the outside masses cannot exceed the weight of the middle mass, or else the system will not be in equilibrium. Additionally, friction and other external forces can reduce the system's efficiency and lifting capacity.

5. What are the limitations of a 2 pulley system with three masses?

One limitation of a 2 pulley system with three masses is that it relies on ideal conditions, such as frictionless pulleys and no external forces. In reality, these conditions are difficult to achieve, which can affect the accuracy and efficiency of the system. Additionally, the lifting capacity is limited, and the system may not be suitable for lifting extremely heavy objects.

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